Displaying similar documents to “An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices”

On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems

Aldo Bressan (1988)

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

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See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case Σ , χ and M satisfy conditions (11.7) when 𝒬 is a polynomial in γ ˙ , conditions (C)-i.e. (11.8) and (11.7) with 𝒬 0 -are proved to be necessary for treating satisfactorily Σ 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....

On Lagrangian systems with some coordinates as controls

Franco Rampazzo (1988)

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

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Let Σ be a constrained mechanical system locally referred to state coordinates ( q 1 , , q N , γ 1 , , γ M ) . Let ( γ ~ 1 γ ~ M ) ( ) be an assigned trajectory for the coordinates γ α and let u ( ) be a scalar function of the time, to be thought as a control. In [4] one considers the control system Σ γ ^ , which is parametrized by the coordinates ( q 1 , , q N ) and is obtained from Σ by adding the time-dependent, holonomic constraints γ α = γ ^ α ( t ) := γ ~ α ( u ( t ) ) . More generally, one can consider a vector-valued control u ( ) = ( u 1 , , u M ) ( ) which is directly identified with γ ^ ( ) = ( γ ^ 1 , , γ ^ M ) ( ) . If one denotes the momenta...

Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín, Håkan Hedenmalm, Alfonso Montes-Rodríguez (2014)

Journal of the European Mathematical Society

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For a smooth curve Γ and a set Λ in the plane 2 , let A C ( Γ ; Λ ) be the space of finite Borel measures in the plane supported on Γ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on Λ . Following [12], we say that ( Γ , Λ ) is a Heisenberg uniqueness pair if A C ( Γ ; Λ ) = { 0 } . In the context of a hyperbola Γ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Λ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly...

Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Kristóf Szarvas, Ferenc Weisz (2016)

Czechoslovak Mathematical Journal

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The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces L p ( d ) (in the case p > 1 ), but (in the case when 1 / p ( · ) is log-Hölder continuous and p - = inf { p ( x ) : x d } > 1 ) on the variable Lebesgue spaces L p ( · ) ( d ) , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type ( 1 , 1 ) . In the present note we generalize Besicovitch’s covering theorem for the so-called γ -rectangles. We introduce a general maximal operator M s γ , δ and with the help of generalized Φ -functions, the strong-...

A characterization of reflexive spaces of operators

Janko Bračič, Lina Oliveira (2018)

Czechoslovak Mathematical Journal

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We show that for a linear space of operators ( 1 , 2 ) the following assertions are equivalent. (i) is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = ( ψ 1 , ψ 2 ) on a bilattice Bil ( ) of subspaces determined by with P ψ 1 ( P , Q ) and Q ψ 2 ( P , Q ) for any pair ( P , Q ) Bil ( ) , and such that an operator T ( 1 , 2 ) lies in if and only if ψ 2 ( P , Q ) T ψ 1 ( P , Q ) = 0 for all ( P , Q ) Bil ( ) . This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.

Optimal estimates for the fractional Hardy operator

Yoshihiro Mizuta, Aleš Nekvinda, Tetsu Shimomura (2015)

Studia Mathematica

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Let A α f ( x ) = | B ( 0 , | x | ) | - α / n B ( 0 , | x | ) f ( t ) d t be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that A α is bounded from L p to L p α with p α = n p / ( α p - n p + n ) when n(1-1/p) < α ≤ n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a ’source’ space S α , Y , which is strictly larger than X, and a ’target’ space T Y , which is strictly smaller than Y, under the assumption that A α is bounded from X into Y and the Hardy-Littlewood...

The weak type inequality for the Walsh system

Ushangi Goginava (2008)

Studia Mathematica

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The main aim of this paper is to prove that the maximal operator σ is bounded from the Hardy space H 1 / 2 to weak- L 1 / 2 and is not bounded from H 1 / 2 to L 1 / 2 .

Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Imed Feki, Ameni Massoudi (2024)

Czechoslovak Mathematical Journal

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We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces H k , p ( G ) , where k * , 1 p and G is either the open unit disk 𝔻 or the annular domain G s , 0 < s < 1 of the complex space . More precisely, we study the behavior on the interior of G of any function f belonging to the unit ball of the Hardy-Sobolev spaces H k , p ( G ) from its behavior on any open connected subset I of the boundary G of G with respect to the L 1 -norm. Our results can be viewed as an improvement and generalization of...

Some weighted norm inequalities for a one-sided version of g * λ

L. de Rosa, C. Segovia (2006)

Studia Mathematica

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We study the boundedness of the one-sided operator g λ , φ between the weighted spaces L p ( M ¯ w ) and L p ( w ) for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of g λ , φ . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of g λ , φ from L p ( ( M ¯ ) [ p / 2 ] + 1 w ) to L p ( w ) , where ( M ¯ ) k denotes the operator M¯ iterated k times.

Isomorphisms and several characterizations of Musielak-Orlicz-Hardy spaces associated with some Schrödinger operators

Sibei Yang (2015)

Czechoslovak Mathematical Journal

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Let L : = - Δ + V be a Schrödinger operator on n with n 3 and V 0 satisfying Δ - 1 V L ( n ) . Assume that ϕ : n × [ 0 , ) [ 0 , ) is a function such that ϕ ( x , · ) is an Orlicz function, ϕ ( · , t ) 𝔸 ( n ) (the class of uniformly Muckenhoupt weights). Let w be an L -harmonic function on n with 0 < C 1 w C 2 , where C 1 and C 2 are positive constants. In this article, the author proves that the mapping H ϕ , L ( n ) f w f H ϕ ( n ) is an isomorphism from the Musielak-Orlicz-Hardy space associated with L , H ϕ , L ( n ) , to the Musielak-Orlicz-Hardy space H ϕ ( n ) under some assumptions on ϕ . As applications, the author further...

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Moshe Marcus, Laurent Véron (2004)

Journal of the European Mathematical Society

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Let Ω be a bounded domain of class C 2 in N and let K be a compact subset of Ω . Assume that q ( N + 1 ) / ( N 1 ) and denote by U K the maximal solution of Δ u + u q = 0 in Ω which vanishes on Ω K . We obtain sharp upper and lower estimates for U K in terms of the Bessel capacity C 2 / q , q ' and prove that U K is σ -moderate. In addition we describe the precise asymptotic behavior of U K at points σ K , which depends on the “density” of K at σ , measured in terms of the capacity C 2 / q , q ' .

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

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We consider the equation - y ' ( x ) + q ( x ) y ( x - ϕ ( x ) ) = f ( x ) , x , where ϕ and q ( q 1 ) are positive continuous functions for all x and f C ( ) . By a solution of the equation we mean any function y , continuously differentiable everywhere in , which satisfies the equation for all x . We show that under certain additional conditions on the functions ϕ and q , the above equation has a unique solution y , satisfying the inequality y ' C ( ) + q y C ( ) c f C ( ) , where the constant c ( 0 , ) does not depend on the choice of f .