Normability of gamma spaces

Filip Soudský

Displaying similar documents to “Normability of gamma spaces”

Some new Formulas involving $Γ_{q}$ Functions

Thomas Ernst (2007)

Rendiconti del Seminario Matematico della Università di Padova

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Order convexity and concavity of Lorentz spaces $Λ_{p, w}$ , 0 < p < ∞

Anna Kamińska, Lech Maligranda (2004)

Studia Mathematica

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We study order convexity and concavity of quasi-Banach Lorentz spaces $Λ_{p, w}$ , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that $Λ_{p, w}$ contains an order isomorphic copy of $l^{p}$ . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for $Λ_{p, w}$ . We conclude with a characterization of the type and cotype of $Λ_{p, w}$ in the case when $Λ_{p, w}$ is a normable space.

Lacunary series in $Q_{K}$ spaces

Hasi Wulan, Kehe Zhu (2007)

Studia Mathematica

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Under mild conditions on the weight function K we characterize lacunary series in the so-called $_{K}$ spaces.

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.

On a fixobject property for $l^{c} β$ -semigroupoids

M. Đurić (1973)

Matematički Vesnik

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

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 $\Sigma$ , $\chi$ and $M$ satisfy conditions (11.7) when $\mathcal{Q}$ is a polynomial in $\dot{\gamma}$ , conditions (C)-i.e. (11.8) and (11.7) with $\mathcal{Q}\equiv 0$ -are proved to be necessary for treating satisfactorily $\Sigma$ 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....

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 $ℝ^{2}$ , 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...

On spirallike functions of order $α$ and type $β$ with fixed second coefficient

M. K. Aouf (1988)

Matematički Vesnik

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Remarks on the critical Besov space and its embedding into weighted Besov-Orlicz spaces

Hidemitsu Wadade (2010)

Studia Mathematica

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We present several continuous embeddings of the critical Besov space $B_{p}^{n / p, ρ} (ℝ ⁿ)$ . We first establish a Gagliardo-Nirenberg type estimate ${| | u | |}_{Ḃ_{q, w_{r}}^{0, ν}} \leq C ₙ {(1 / (n - r))}^{1 / q + 1 / ν - 1 / ρ} {(q / r)}^{1 / ν - 1 / ρ} {| | u | |}_{Ḃ_{p}^{0, ρ}}^{(n - r) p / n q} {| | u | |}_{Ḃ_{p}^{n / p, ρ}}^{1 - (n - r) p / n q}$ , for 1 < p ≤ q < ∞, 1 ≤ ν < ρ ≤ ∞ and the weight function $w_{r} (x) = 1 / {(| x |}^{r})$ with 0 < r < n. Next, we prove the corresponding Trudinger type estimate, and obtain it in terms of the embedding $B_{p}^{n / p, ρ} (ℝ ⁿ) ↪ B_{Φ ₀, w_{r}}^{0, ν} (ℝ ⁿ)$ , where the function Φ₀ of the weighted Besov-Orlicz space $B_{Φ ₀, w_{r}}^{0, ν} (ℝ ⁿ)$ is a Young function of the exponential type. Another point of interest is to embed $B_{p}^{n / p, ρ} (ℝ ⁿ)$ into the weighted Besov...

An application of the method wherein the $p h i$ - and $c h i$ - methods are combined for the determination of the grating constant. [II.]

Swami Jnanananda (1936)

Časopis pro pěstování matematiky a fysiky

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Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl (2014)

Studia Mathematica

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We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space $^{(ω)}$ and the Roumieu space $^{ω}$ as intersection and union of spaces $^{(M)}$ and $^{M}$ for associated weight sequences, respectively.

On the equation $ϕ (x + m) = ϕ (x) + m$

A. Makowski (1964)

Matematički Vesnik

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A weighted inequality for the Hardy operator involving suprema

Pavla Hofmanová (2016)

Commentationes Mathematicae Universitatis Carolinae

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Let $u$ be a weight on $(0, \infty)$ . Assume that $u$ is continuous on $(0, \infty)$ . Let the operator $S_{u}$ be given at measurable non-negative function $ϕ$ on $(0, \infty)$ by $S_{u} ϕ (t) = sup_{0 < τ \leq t} u (τ) ϕ (τ) .$ We characterize weights $v, w$ on $(0, \infty)$ for which there exists a positive constant $C$ such that the inequality ${(\int_{0}^{\infty} {[S_{u} ϕ (t)]}^{q} w (t) d t)}^{\frac{1}{q}} ≲ {(\int_{0}^{\infty} {[ϕ (t)]}^{p} v (t) d t)}^{\frac{1}{p}}$ holds for every $0 < p, q < \infty$ . Such inequalities have been used in the study of optimal Sobolev embeddings and boundedness of certain operators on classical Lorenz spaces.

Embedding in $T_{3}$ - $F_{σ}$ spaces

D. W. Hajek, I. Irizarry (1981)

Matematički Vesnik

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The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

Matematički Vesnik

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$L_{p, q}$ spaces

Joseph Kupka

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CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the $L_{p, q}$ spaces................................. 114. Integral representation of bounded linear functionals on $L_{p, q} (B)$ ........ 235. Examples in $L_{p, q}$ theory...................................................................................

The existence of $P (α)$ -points of N* for $ℵ_{0} α < 𝔠$

A. Szymański (1977)

Colloquium Mathematicae

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On C $^{*}$ -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

Annales Polonici Mathematici

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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