首页/论文/math/0206109

arXiv math/02061092002-06math.FA

On P. Levy's Stable Laws and Reflexive Subspaces of the Banach space L of Lebesgue summable functions on [0,1]

Eugene Tokarev

备注：: Latex2e; revised version

英文摘要：

To describe a set of functions, which forms a reflexive subspace B of the classical Banach space L a special function that characterizes their average integral growth is introduced. It is shown that this function essentially depends on the geometry of B. By the way, one question of la Vallee Poussin is answered. Also a short proof of the known result about the existence of an uncomplemented subspace isomorphic to the Hilbert space in every Lebesgue - Riesz space Lp (1<p<2) is obtained.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

非反射Lebesgue空间上平均算子的紧致性

Compactness of averaging operators on non-reflexive Lebesgue spaces

Faculty of Engineering, Kanagawa University（神奈川大学工学部）

本文研究非反射Lebesgue空间上平均算子的紧致性条件，基于度量与测度的均匀连续性及倍增性质给出等价条件。

2026-02-25math.FA

Generalized vectorial Lebesgue and Bochner integration theory

This paper contains a development of the Theory of Lebesgue and Bochner spaces of summable functions. It represents a synthesis of the results due to H. Lebesgue, S. Banach, S. Bochner, G. Fubini, S. Saks, F. Riesz, N. Dunford, P. Halmos, and other contributors to this theory. The construction of the theory is based on the notion of a measure on a prering of sets in any abstract space X. No topological structure of the space X is required for the development of the theory. Measures on prerings generalize the notion of abstract Lebesgue measures. These measures are readily available and it is n…

2010-06-19math.FA

Fixed Point Properties and reflexivity in Variable Lebesgue Spaces

In this paper the weak fixed point property ($w$-FPP) and the fixed point property (FPP) in Variable Lebesgue Spaces are studied. Given $(Ω,Σ,μ)$ a $σ$-finite measure and $p(\cdot)$ a variable exponent function, the $w$-FPP is completely characterized for the variable Lebesgue space $L^{p(\cdot)}(Ω)$ in terms of the exponent function $p(\cdot)$ and the absence of an isometric copy of $L_1[0,1]$. In particular, every reflexive $L^{p(\cdot)}(Ω)$ has the FPP and our results bring to light the existence of some nonreflexive variable Lebesgue spaces satisfying the $w$-FPP, in sharp contrast with th…

2020-10-06math.FA

关于唯一$\ell_{1}$扩散模型的完全分离及Banach空间的Lebesgue性质

On the complete separation of unique $\ell_{1}$ spreading models and the Lebesgue property of Banach spaces

University of North Texas（北德克萨斯大学）；York University（约克大学）

本文构造了一个反射Banach空间，其扩散模型与$\ell_1$的单位向量基均匀等价，但其所有无限维闭子空间均不满足Lebesgue性质。

2024-08-27math.FA

On Henri Cartan's vectorial mean-value theorem and its applications to Lipschitzian operators and generalized Lebesgue-Bochner-Stieltjes integration theory

H. Cartan in his book on differential calculus proved a theorem generalizing a Cauchy's mean-value theorem to the case of functions taking values in a Banach space. Cartan used this theorem in a masterful way to develop the entire theory of differential calculus and theory of differential equations in finite and infinite dimensional Banach spaces. The author proves a generalization of this theorem to the case when the inequality involving the derivatives holds everywhere with exception of a set of Lebesgue measure zero, and the derivatives are replaced by weaker derivatives. Namely the right-s…

2009-10-13math-phmath.FAmath.MP

On the reflexivity properties of Banach bundles and Banach modules

In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $σ$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its $L^p$-sections is uniformly convex for every $p\in(1,\infty)$. - The fibers of a bundle are reflexive if and only if the space of its $L^p$-sections is reflexive. These results generalise the well-known corresponding ones for Lebesgue-Bochner spaces.

2022-09-29math.FA

更多相关论文收起更多论文

On the reflexivity of the spaces of variable integrability and summability

In this paper, we show that under the condition $ 1<p_-, q_-, p_+, q_+<\infty$, the space $\ell^{q(\cdot)} (L^{p(\cdot)})$ is reflexive. In this way we give an answer to open problem posed by Hästö in 2017 about the reflexivity of the variable mixed Lebesgue-sequence spaces $\ell^{q(\cdot)} (L^{p(\cdot)})$. What is important here is that the dual space of $\ell^{q(\cdot)} (L^{p(\cdot)})$ is specified. As its direct corollary, we show that the corresponding Besov space $B^{s(\cdot)}_{p(\cdot)q(\cdot)}$ is reflexive.

2022-03-26math.FA

The UMD property for Musielak--Orlicz spaces

In this paper we show that Musielak--Orlicz spaces are UMD spaces under the so-called $Δ_2$ condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak--Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that reflexive variable Lebesgue spaces $L^{p(\cdot)}$ are UMD spaces.

2018-11-09math.FAmath.PR

Envelopes in Banach spaces

We define the notion of isometric envelope of a subspace in a Banach space, and relate it to a) the mean ergodic projection on the space of fixed points of a semigroup of contractions, b) results on Korovkin sets from the 70's, and c) extension properties of linear isometric embeddings. We use this concept to address the recent conjecture that the Gurarij space and the spaces $L_p$, $p \notin 2\mathbb N+4$ are the only separable Approximately Ultrahomogeneous Banach spaces (a certain multidimensional transitivity of the action of the linear isometry group). The similar conjecture for Fraïssé B…

2021-12-22math.FA

作用于某些Banach函数空间上具有连续符号的Wiener-Hopf算子的Fredholm准则

Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces

本文将Duduchava在1970年代关于Lebesgue空间上具有连续符号的Wiener-Hopf算子的Fredholm准则，推广至Lorentz、自反Orlicz和变Lebesgue空间三种Banach函数空间。

2025-09-17math.FA

A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain

The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in the complex plane. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the clos…

2016-07-05math.FA

Note on vector valued Hardy spaces related to analytic functions having distributional boundary values

Analytic functions defined on a tube domain $T^{C}\subset \mathbb{C}^{n}$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^{p}(T^{C},X)$ if the boundary value is in the vector valued Lebesgue space $L^{p}(\mathbb{R}^{n},X)$, where $1\leq p \leq \infty$ and $C$ is a regular open convex cone. Poisson integral transform representations of elements of $H^{p}(T^{C}, X)$ are also obtained for certain classes of Banach spaces, including reflexive Banach spaces.

2020-01-27math.CVmath.FA

Spaces of measurable functions on the the Levi-Civita field

We introduce the $\mathcal{L}^p$ spaces of measurable functions whose $p$-th power is summable with respect to the uniform measure over the Levi-Civita field $\mathcal{R}$. These spaces are the counterparts of the real $L^p$ spaces based upon the Lebesgue measure. Nevertheless, they lack some properties of the $L^p$ spaces: for instance, the $\mathcal{L}^p$ spaces are not complete with respect to the $p$-norm. This motivates the study of the completions of the $\mathcal{L}^p$ spaces with respect to strong convergence, denoted by $\mathcal{L}_s^p$. It turns out that the $\mathcal{L}_s^p$ spaces…

2020-06-12math.FA

巴拿赫空间上有界算子构成的巴拿赫代数的极大右理想

Maximal right ideals of the Banach algebra of bounded operators on a Banach space

Czech Academy of Sciences（捷克科学院）；Institute of Mathematics and Computer Science Jagiellonian University（雅盖隆大学数学与计算机科学研究所）；Lancaster University（兰卡斯特大学）

该研究探讨巴拿赫代数$\boldsymbol{\beta}(E)$的极大右理想，明确有限生成提升理想的算子论障碍，通过相关方法对多类巴拿赫空间构造非有限生成极大右理想，还确定部分空间的有限生成极大右理想均为固定的。

2026-08-24math.FA

The $L^p$ primitive integral

For each $1\leq p<\infty$ a space of integrable Schwartz distributions, $L^'^{\,p}$, is defined by taking the distributional derivative of all functions in $L^p$. Here, $L^p$ is with respect to Lebesgue measure on the real line. If $f\in L^'^{\,p}$ such that $f$ is the distributional derivative of $F\in L^p$ then the integral is defined as $\int^\infty_{-\infty} fG=-\int^\infty_{-\infty} F(x)g(x)\,dx$, where $g\in L^q$, $G(x)= \int_0^x g(t)\,dt$ and $1/p+1/q=1$. A norm is $\lVert f\rVert'_p=\lVert F\rVert_p$. The spaces $L^'^{\,p}$ and $L^p$ are isometrically isomorphic. Distributions in $L^'^…

2012-08-17math.CAmath.FA

由算子分数次幂生成的整群

Entire groups generated by fractional powers of operators

Universidad de Zaragoza（萨拉戈萨大学）

研究由分数次幂算子$-(I-T)^a$生成的整群，引入多项式族$(p_{n;a})$并给出其递推关系，证明其属于$\ell^1$空间，并与Lévy密度函数相关，最后讨论特例及应用。

2026-06-16math.CVmath.FA