$L^p$Regularity of Transmission Problems in Dihedral Domains

Aissa Aibeche; Wided Chikouche; Serge Nicaise

Displaying similar documents to “ $L^{p}$ Regularity of Transmission Problems in Dihedral Domains”

A Regular Threefold of General Type with $p_{g}=0$ and $P_{2}=6$

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g}=0$ : The examples in the literature have $P_{2}\leq 5$ . In the present paper we present a non-singular threefold with $p_{g}=q_{1}=q_{2}=0$ ; $P_{2}=6$ ; the bicanonical map is stably birational.

A Note on Sectorial and R-Sectorial Operators

Alberto Venni (2008)

Bollettino dell'Unione Matematica Italiana

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The following results are proved: (i) if $\alpha$ , $\beta\in\mathbb{R}^{+}$ and $A$ is a sectorial operator, then the set $\{t^{\alpha}A^{\beta}(t+A);t>0\}$ is bounded; (ii) the same set of operators is R-bounded if $A$ is R-sectorial.

$L^{p}$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$

Ralph Chill, Sachi Srivastava (2008)

Bollettino dell'Unione Matematica Italiana

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If the second order problem $\ddot{u}+\dot{u}+Au=f$ has $L^{p}$ maximal regularity for some $p\in(1,\infty)$ , then it has $L^{p}$ maximal regularity for every $p\in(1,\infty)$ .

Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$

A. M. Mantero, A. Zappa (2009)

Bollettino dell'Unione Matematica Italiana

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Let $\Delta$ be thick affine building of type $\widetilde{G}_{2}$ the Laplace operators of $\Delta$ ; associated with a pair $(y_{1},y_{2})$ ; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$ ; by using only the combinatorial structure of $\Delta$ .

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let $D$ be an integral domain with quotient field $D$ . Recall that $D$ is Schreier if $D$ is integrally closed and for all $x,y,z\in D\setminus\{0\}$ , $x|yz$ implies that $x=r\cdot s$ where $r|y$ e $s|z$ . A GCD domain is Schreier. We show that an integral domain $D$ is a GCD domain if and only if (i) for each pair $a,b\in D\setminus\{0\}$ , there is a finitely generated ideal $B$ such that $aD\bigcap bD=B_{v}$ and (ii) every quadratic in $D[X]$ that is a product of two linear polynomials in $K[X]$ is a product of two linear polynomials in $D[X]$ . We also show that $D$ is Schreier if and only if every...

A New $L^{1}$ -Lower Semicontinuity Result

Daniele Graziani (2007)

Bollettino dell'Unione Matematica Italiana

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The aim of this work is to prove a chain rule and an $L^{1}$ -lower semicontinuity theorems for integral functional defined on $BV(\Omega)$ . Moreover we apply this result in order to obtain new relaxation and $\Gamma$ -convergence result without any coerciveness and any continuity assumption of the integrand $f(x,s,p)$ with respect to the variable $s$ .

Conductor and separating degrees for sets of points in $\mathbb{P}^{r}$ and in $\mathbb{P}^{1}\times\mathbb{P}^{1}$

Lucia Marino (2006)

Bollettino dell'Unione Matematica Italiana

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We attempt to generalize conductor degree's results, known in $\mathbb{P}^{2}$ , to the case of 0-dimensional schemes of $\mathbb{P}^{r}$ . In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in $\mathbb{P}^{r}$ and we determine the conductor degree of every point in a $r$ -partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...

The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt}(p+1)$

Marilena Massa (2007)

Bollettino dell'Unione Matematica Italiana

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We study the irreducibility of the Dirichlet polynomial $P_{G}(s)$ when $G$ is the alternating group on $p+1$ elements with $p$ prime and we prove that $P_{G}(s)$ is irreducible for infinitely many choiches of $p$ .

Some Separation Axioms Via Ideals

D. Sivaraj, V. Renuka Devi (2007)

Bollettino dell'Unione Matematica Italiana

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We introduce a new class of spaces, called Hausdorff modulo $\mathcal{I}$ or $T_{2}$ mod $\mathcal{I}$ spaces with respect to an ideal $\mathcal{I}$ which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal $\mathcal{I}$ was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of $\mathcal{I}$ -compact subsets in Hausdorff modulo $\mathcal{I}$ spaces and generalize some results of Hamlett and Jankovic....

On Relative $\gamma_{k}$ -Sets

Maddalena Bonanzinga, Filippo Cammaroto, Bruno A. Pansera (2007)

Bollettino dell'Unione Matematica Italiana

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In this note we show a relative version of $\gamma_{k}$ -set introduced and studied in [12]. We give several characterizations of this property; in particular one of the characterizations is Ramsey theoretical. Also we give a result involving a property of the corresponding mapping between function spaces.

Isomorphisms of Royden Type Algebras Over $\mathbb{S}^{1}$

Teresa Radice, Eero Saksman, Gabriella Zecca (2009)

Bollettino dell'Unione Matematica Italiana

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Let $\mathbb{S}^{1}$ and $\mathbb{D}$ be the unit circle and the unit disc in the plane and let us denote by $\mathcal{A}(\mathbb{S}^{1})$ the algebra of the complex-valued continuous functions on $\mathbb{S}^{1}$ which are traces of functions in the Sobolev class $W^{1,2}(\mathbb{D})$ . On $\mathcal{A}(\mathbb{S}^{1})$ we define the following norm $\|u\|=\|u\|_{L^{\infty}(\mathbb{S}^{1})}+\left(\iint_{\mathbb{D}}|\nabla\tilde% {u}|^{2}\right)^{1/2}$ where is the harmonic extension of $u$ to $\mathbb{D}$ . We prove that every isomorphism of the functional algebra $\mathcal{A}(\mathbb{S}^{1})$ is a quasitsymmetric change of variables on $\mathbb{S}^{1}$ .

Inverse results for generalized Favard-Kantorovich and Favard-Durrmeyer operators in weighted function spaces

Nowak Grzegorz (2006)

Bollettino dell'Unione Matematica Italiana

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We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions $f$ such that $w_{2m}f\in L^{p}(R)$ , where $1\leq p\leq\infty$ and $w_{2m}(x)=(1+x^{2m})^{-1}$ , $m\in N_{0}$ .

Congruences between modular forms and related modules

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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We fix $\ell$ a prime and let $M$ be an integer such that $\ell\operatorname{\not|}M$ ; let $f\in S_{2}(\Gamma_{1}(M\ell^{2}))$ be a newform supercuspidal of fixed type at $\ell$ and special at a finite set of primes. For an indefinite quaternion algebra over $Q$ , of discriminant dividing the level of $f$ , there is a local quaternionic Hecke algebra $T$ associated to $f$ . The algebra $T$ acts on a module $M_{f}$ coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, $T$ is the universal deformation ring of a global...

A Montel Type Result for Subharmonic Functions

R. Supper (2009)

Bollettino dell'Unione Matematica Italiana

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This article is devoted to sequences $(u_{n})_{n}$ of subharmonic functions in $\mathbb{R}^{N}$ , with finite order, whose means $J_{u_{n}}(r)$ (over spheres centered at the origin, with radius r) satisfy such a condition as: $\forall r>0$ , $\exists A_{r}>0$ such that $J_{u_{n}}(r)\leq A_{r}$ , $\forall n\in\mathbf{N}$ . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.

Eisenstein ideal and reducible $\lambda$ -adic Representations Unramified Outside a Finite Number of Primes.

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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The object of this note is to study certain 2-dimensional $\lambda$ -adic representations of $\operatorname{Gal}(\bar{Q}/Q)$ ; fixed $p_{1},\ldots,p_{n}$ distinct primes, we will consider representations $\rho\colon G\to GL_{2}(A)$ , given by the matrix $\rho=\left(\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}\right)$ which are unramified outside $p_{1},\ldots,p_{n},\infty$ and the residue characteristic of $\lambda$ , which are a product of $m$ representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo $\lambda$ . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...

Correctors for Parabolic Equations in a Heterogeneous Fibered Medium

Mourad Sfaxi, Ali Sili (2007)

Bollettino dell'Unione Matematica Italiana

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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium $\Omega$ made of two materials. The first one is located in a set $F_{\epsilon}$ of cylindrical parallel fibers periodically distributed with a period of size $\epsilon$ , and the second one is located in the "matrix" $M_{\epsilon}=\Omega\setminus F_{\epsilon}$ . The ratio between the conductivity coefficients of the two materials is of order $1/\epsilon^{2}$ . After writing the homogenized problem, we give a corrector result and prove...

The Martingale Problem in Hilbert Spaces

Giuseppe Da Prato, Luciano Tubaro (2008)

Bollettino dell'Unione Matematica Italiana

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We consider an SPDE in a Hilbert space $H$ of the form $dX(t)=(AX(t)+b(X(t)))\,dt+\sigma(X(t))\,dW(t)$ , $X(0)=x\in H$ and the corresponding transition semigroup $P_{t}f(x)=\mathbb{E}[f(X(t,x))]$ . We define the infinitesimal generator $\bar{L}$ of $P_{t}$ through the Laplace transform of $P_{t}$ as in [1]. Then we consider the differential operator $L\varphi=\frac{1}{2}\operatorname{Tr}[\sigma(x)\sigma^{*}(x)D^{2}\varphi]+% \langle b(x),D\varphi\rangle$ defined on a suitable set $V$ of regular functions. Our main result is that if $V$ is a core for $\bar{L}$ , then there exists a unique solution of the martingale problem defined in terms of $L$ . Application to the Ornstein-Uhlenbeck equation and to some regular...

On the projective genus of surfaces

Pietro Sabatino (2006)

Bollettino dell'Unione Matematica Italiana

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Let $X\subset\mathbb{P}^{N}$ be a smooth irreducible non degenerate surface over the complex numbers, $N\geq 4$ . We define the projective genus of $X$ , denoted by $PG(X)$ , as the geometric genus of the singular curve of the projection of $X$ from a general linear subspace of codimension four. Denote by $g(X)$ the sectional genus of $X$ . In this paper we conjecture that the only surfaces for which $PG(X)=g(X)-1$ are the del Pezzo surface in $\mathbb{P}^{4}$ , in $\mathbb{P}^{5}$ and a conic bundle of degree 5 in $\mathbb{P}^{4}$ . We prove that for $N\geq 5$ if $PG(X)=g(X)-1+\lambda$ , $\lambda$ a non negative integer, then $g(X)\leq\lambda+1+\alpha$ where...

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si considera l’equazione astratta $BA_{1}u+A_{0}u=h$ , dove $A_{i}$ $(i=0,1)$ e $B$ sono convenienti operatori lineari chiusi fra spazi di Banach, $A_{i}$ non è necessariamente invertibile, e $A_{0}$ , $A_{1}$ non commutano con $B$ . Si studiano esistenza ed unicità delle soluzioni. Si indicano alcune applicazioni a certe equazioni differenziali degeneri o singolari.

A Sufficient Condition for the $C^{2}$ -Rectifiability of the Set of Regular Values (in the Sense of Clarke) of a Lipschitz Map

Silvano Delladio (2008)

Bollettino dell'Unione Matematica Italiana

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We prove a result about the rectifiability of class $C^{2}$ of the set of regular values (in the sense of Clarke) of a Lipschitz map $\varphi\colon\mathbb{R}^{n}\rightarrow\mathbb{R}^{N}$ with $n<N$

A Note on $\mathcal{R}$ -Maps

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

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Richness of the class of $\mathcal{R}$ -maps [3] is investigated. Several consequences for the theory of quasi- $\mathcal{H}$ -closed spaces are indicated.

Cohomology of Tango bundle on $\mathbb{P}^{5}$

Daniele Faenzi (2006)

Bollettino dell'Unione Matematica Italiana

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The Tango bundle $T$ is defined as the pull-back of the Cayley bundle over a smooth quadric $Q_{5}$ in $\mathbb{P}_{6}$ via a map $f$ existing only in characteristic 2 and factorizing the Frobenius $\varphi$ . The cohomology of $T$ is computed in terms of $S\otimes C$ , $\varphi^{*}(C)$ , $\text{Sym}^{2}(C)$ and $C$ , which we handle with Borel-Bott-Weil theorem.

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Convergence to Equilibrium of the Solution of Kac's Kinetic Equation. A Probabilistic View

Eugenio Regazzini (2009)

Bollettino dell'Unione Matematica Italiana

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Let $f(\cdot,t)$ be the probability density function representing the solution of Kac's Boltzmann-like equation at time $t$ , with initial data $f_{0}$ , and let $g_{\sigma}$ be the Gaussian density with zero mean and variance $\sigma^{2}$ , $\sigma^{2}$ being the value of the second moment of $f_{0}$ . Henry McKean Jr. put forward the conjecture that the total variation distance between $f(\cdot,t)$ and $g_{\sigma}$ goes to zero, as $t\to+\infty$ , with an exponential rate equal to $-1/4$ . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...

Existence and uniqueness for an integro-differential equation with singular kernel

Valeria Berti (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper we study the evolutive problem of linear viscoelasticity with a singular kernel memory $G^{\prime}$ . We assume that $G^{\prime}$ presents an initial singularity, so that it is not a $L^{1}$ -function in time, whereas the relaxation function $G$ is integrable at $t=0$ . By applying the Fourier transform method, we prove a theorem of existence and uniqueness of the weak solutions in a functional space whose definition is strictly related to the properties of the kernel memory.

Geometry of Syzygies via Poncelet Varieties

Giovanna Ilardi, Paola Supino, Jean Vallès (2009)

Bollettino dell'Unione Matematica Italiana

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We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$ -dimensional linear subspaces of $V_{n}=H^{0}(\mathbb{P}^{1},\mathcal{O}_{\mathbb{P}_{1}}(n))$ . We define $\mathfrak{X}_{k,r,d}$ as the classifying space of the $k$ -dimensional linear systems of degree $n$ on $\mathbb{P}^{1}$ , whose bases realize a fixed number $r$ of polynomial relations of fixed degree $d$ , say $r$ syzygies of degree $d$ . Firstly, we compute the dimension of $\mathfrak{X}_{k,r,d}$ . In the second part we make a link between $\mathfrak{X}_{k,r,d}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the...

Relaxation and gamma-convergence of supremal functionals

Francesca Prinari (2006)

Bollettino dell'Unione Matematica Italiana

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We prove that the $\Gamma$ -limit in $L^{\infty}_{\mu}$ of a sequence of supremal functionals of the form $F_{k}(u)=\operatorname{\mu-ess\,sup}_{\Omega}f_{k}(x,u)$ is itself a supremal functional. We show by a counterexample that, in general, the function which represents the $\Gamma$ -lim $F(\cdot,B)$ of a sequence of functionals $F_{k}(u,B)=\operatorname{\mu-ess\,sup}_{B}f_{k}(x,u)$ can depend on the set $B$ and wegive a necessary and sufficient condition to represent $F$ in the supremal form $F(u,B)=\operatorname{\mu-ess\,sup}_{B}f(x,u)$ . As a corollary, if $f$ represents a supremal functional, then the level convex envelope of $f$ represents its weak* lower semicontinuous envelope. ...

Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type $B_{d}$

Francesca Vetro (2008)

Bollettino dell'Unione Matematica Italiana

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Let $X$ , $X^{\prime}$ , $Y$ be smooth projective complex curves with $Y$ curve of genus $\geq 1$ . Let $d$ be an integer $\geq 3$ , let $\underline{e}=(e_{1},\ldots,e_{r})$ be a partition of $d$ and let $|e|=\sum_{i=1}^{r}(e_{i}-1)$ . Let $X\xrightarrow{\pi}X^{\prime}\xrightarrow{f}Y$ be a sequence of coverings where $\pi$ is a degree 2 branched covering and $f$ is a degree $d$ covering, with monodromy group $S_{d}$ , branched in $n_{2}+1$ points, one of which is special point $c$ whose local monodromy has cycle type given by $\underline{e}$ . Moreover the branch locus of the covering $\pi$ is contained in $f^{-1}(c)$ . In this paper we prove the irreducibility...

A Result About $C^{2}$ -Rectifiability of One-Dimensional Rectifiable Sets. Application to a Class of One-Dimensional Integral Currents

Silvano Delladio (2007)

Bollettino dell'Unione Matematica Italiana

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Let $\gamma,\tau\colon[a,b]\rightarrow R^{k+1}$ be a couple of Lipschitz maps such that $\gamma^{\prime}=\pm|\gamma^{\prime}|\tau$ almost everywhere in $[a,b]$ . Then $\gamma([a,b])$ is a $C^{2}$ -rectifiable set, namely it may be covered by countably many curves of class $C^{2}$ embedded in $R^{k+1}$ . As a conseguence, projecting the rectifiable carrier of a one-dimensional generalized Gauss graph provides a $C^{2}$ -rectifiable set.

On non-Uniqueness of Complex Geodesies in Convex Bounded Domains

Graziano Gentili (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di $\mathbb{C}$ in un dominio convesso limitato $D$ di uno spazio di Banach complesso $E$ , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di $D$ .

On the Dirichlet Problem with Orlicz Boundary Data

Gabriella Zecca (2007)

Bollettino dell'Unione Matematica Italiana

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Let us consider a Young's function $\Phi\colon\mathbb{R}^{+}\to\mathbb{R}^{+}$ satisfying the $\Delta_{2}$ condition together with its complementary function $\Psi$ , and let us consider the Dirichlet problem for a second order elliptic operator in divergence form: $\begin{cases}Lu=0&\text{in }B\\ u_{|\partial B}=f\end{cases}$ $B$ the unit ball of $\mathbb{R}^{n}$ . In this paper we give a necessary and sufficient condition for the $L^{\phi}$ -solvability of the problem, where $L^{\phi}$ is the Orlicz Space generated by the function $\Phi$ . This means solvability for $f\in L^{\Phi}$ in the sense of [5], [8], where the case $\Phi(t)=t^{p}$ is treated. ...

An Elliptic Problem with a Lower Order Term Having Singular Behaviour

Daniela Giachetti, François Murat (2009)

Bollettino dell'Unione Matematica Italiana

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We prove the existence of distributional solutions to an elliptic problem with a lower order term which depends on the solution $u$ in a singular way and on its gradient $D u$ with quadratic growth. The prototype of the problem under consideration is $\begin{cases}-\Delta u+\lambda u=\pm\frac{|Du|^{2}}{|u|^{k}}+f&\text{in}\,% \Omega,\\ u=0&\text{on}\,\partial\Omega,\end{cases}$ where $\lambda>0$ , $k>0$ ; $f(x)\in L^{\infty}(\Omega)$ , $f(x)\geq 0$ (and so $u\geq 0$ ). If $0<k<1$ , we prove the existence of a solution for both the "+" and the "-" signs, while if $k\geq 1$ , we prove the existence of a solution for the "+" sign only.

On locally $S$ -closed spaces

Takashi Noiri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente $S$ -chiuso sia localmente $S$ -chiuso.

Threefolds with Kodaira Dimension 0 or 3

Ezio Stagnaro (2007)

Bollettino dell'Unione Matematica Italiana

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Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in $\mathbb{P}^{4}$ , having the irregularities $q_{1}=q_{2}=0$ and the following periodical sequences of plurigenera respectively $(p_{g},P_{2},P_{3},\ldots,P_{m},\ldots)=(0,0,1,0,0,1,\ldots),(0,0,0,1,0,0,0,1,% \ldots),(0,0,0,0,1,0,0,0,0,1,\ldots).$ In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with $qq_{1}=q_{2}=0,p_{g}=1$ , $P_{2}=2$ whose m-canonical transformation is birational if and only if $m\geq 11$ .

Squarefree Lexsegment Ideals with Linear Resolution

Vittoria Bonanzinga, Loredana Sorrenti (2008)

Bollettino dell'Unione Matematica Italiana

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In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let $M_{d}$ denote the set of all squarefree monomials of degree $d$ in a polynomial ring $k[x_{1},\ldots,x_{n}]$ in $n$ variables over a field $k$ . We order the monomials lexicographically such that $x_{1}>x_{2}>\ldots>x_{n}$ , thus a lexsegment (of degree $d$ ) is a subset of $M_{d}$ of the form $L(u,v)=\{w\in M_{d}:u\geq w\geq v\}$ for some $u,v\in M_{d}$ con $u\geq v$ . An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear...

The equation $\bar{\partial}u=f$ the intersection of pseudoconvex domains

Alessandro Perotti (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Viene studiata l'equazione $\bar{\partial}u=f$ per le forme regolari sulla chiusura dell'intersezione di $k$ domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme $\mathbf{C}^{k}$ .

A curve of genus $q$ with a Half-Canonical embedding in $\mathbf{P}^{3}$

Sevin Recillas (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si costruiscono curve di genere $g=4n—3$ , $n\geq 3$ che hanno $2^{n-3}(2^{n-2}-1)$ fasci semicanonici $L$ tali che $h^{0}(L)=4$ . Per $n+3$ si dimostra che gli $L$ sono molto ampi.

A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces

D. Cruz-Uribe, L. Diening, A. Fiorenza (2009)

Bollettino dell'Unione Matematica Italiana

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We give a new proof using the classic Calderón-Zygmund decomposition that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space $L^{p(\cdot)}$ whenever the exponent function $p(\cdot)$ satisfies log-Hölder continuity conditions. We include the case where $p(\cdot)$ assumes the value infinity. The same proof also shows that the fractional maximal operator $M_{a}$ , $0<a<n$ , maps $L^{p(\cdot)}$ into $L^{q(\cdot)}$ , where $1/p(\cdot)-1/q(\cdot)=a/n$ .

On the Variance Associated to a Family of Ovaloids in the Euclidean Space $E_{3}$

Giuseppe Caristi, Giovanni Molica Bisci (2007)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider a random variable $h$ arising from an intersection problem between a fixed convex body $K_{0}$ and a system of random independent and uniformly distributed ovaloids in $E_{3}$ .

$\bf{L}$ -embedding, Amalgamation and $\bf{L}$ -elementary equivalence

Daniele Mundici (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Ogni logica $L$ genera canonicamente la $L$ -equivalenza $\equiv_{L}$ e la $L$ -immersione $\underset{L}{\rightarrow}$ proprio come la logica del primo ordine genera l’equivalenza elementare $\equiv$ e l’immersione elementare $\lesssim$ . Astraendo da $L$ , è interessante studiare in sè relazioni d’equivalenza e di immersione generali tra strutture. Mostriamo che esiste una corrispondenza biunivoca tra relazioni d’equivalenza con la proprietà di Robinson e relazioni d’immersione con la proprietà di Amalgamazione Forte ( $AP^{+}$ ). Caratterizziamo algebricamente...

On the existence of scrolls in $\bf{P}^{4}$

Antonio Lanteri (1980)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dimostra il seguente risultato. Sia $X$ una superficie proiettivamente rigata, non iperpiana, di $\bf{P}^{4}$ ; allora $X$ è la rigata cubica oppure è una rigata quintica ellittica. Si descrive inoltre una nuova generazione proiettiva delle rigate quintiche ellittiche di $\bf{P}^{4}$ .

A Note on Regular-closed Functions

Takashi Noiri (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Se $X$ ed $Y$ sono spazi topologici, una funzione $f:X\to Y$ è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di $X$ in un insieme chiuso di $Y$ . Si dimostra che una funzione regolarmente chiusa $f:X\to Y$ risulta chiusa se $X$ è normale.

On bibasic systems and a Retherford’s problem

Anatoli Pličko, Paolo Terenzi (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Ogni spazio di Banach ha un sistema bibasico $(x_{n},f_{n})$ normalizzato; inoltre ogni successione $(x_{n})$ uniformemente minimale appartiene ad un sistema biortogonale limitato $(x_{n},f_{n})$ , dove $(f_{n})$ è M-basica e normante.

On the Aronszajn property for integral equations in Banach space

Stanisław Szufla (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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For the integral equation (1) below we prove the existence on an interval $J=[0,a]$ of a solution $x$ with values in a Banach space $E$ , belonging to the class $L^{p}(J,E)$ , $p>1$ . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.

On the abstract Cauchy problem in the case of constant domains

Paolo Acquistapace, Brunello Terreni (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti $u\in\mathbf{C}(\left[0,T\right],E)$ dell'equazione di evoluzione non autonoma $u^{\prime}(t)-A(t)u(t)=f(t)$ con il dato iniziale $u(0)=x$ , in uno spazio di Banach $E$ . Gli operatori $A(t)$ sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da $t$ e non necessariamente denso in $E$ . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.

Remarks on $\mathcal{S}$ -Closedness in Topological Spaces

Zbigniew Duszyński (2007)

Bollettino dell'Unione Matematica Italiana

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Corresponding to [27], some properties of S-closed subspaces and subsets $\mathcal{S}$ -closed relative to a topological space are proved. Conditions under which mappings preserve certain $\mathcal{S}$ -closed subspaces are investigated.

Displaying similar documents to “ L p Regularity of Transmission Problems in Dihedral Domains”

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