可变 Lebesgue 空间中的 Marcinkiewicz-Zygmund 不等式

IF 1.1 2区 数学 Q1 MATHEMATICS
Marcos Bonich, Daniel Carando, Martin Mazzitelli
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引用次数: 0

摘要

我们研究定义在具有可变指数的 Lebesgue 空间上的线性算子的(\ell ^r\)值扩展。在指数的一些自然(和通常)条件下,我们描述了 \(1\le r\le \infty \)的特征,使得每个有界线性算子 \(T:L^{q(\cdot )}(\Omega _2, \mu )\rightarrow L^{p(\cdot )}(\Omega _1, \nu )\) 都有一个有界的\(ell ^r\)-值扩展。我们同时考虑了非原子度量和有原子的度量,并展示了可能出现的差异。我们介绍了我们的结果在线性算子的加权规范不等式和具有粗糙核的分数算子的向量值扩展中的一些应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Marcinkiewicz–Zygmund inequalities in variable Lebesgue spaces

We study \(\ell ^r\)-valued extensions of linear operators defined on Lebesgue spaces with variable exponent. Under some natural (and usual) conditions on the exponents, we characterize \(1\le r\le \infty \) such that every bounded linear operator \(T:L^{q(\cdot )}(\Omega _2, \mu )\rightarrow L^{p(\cdot )}(\Omega _1, \nu )\) has a bounded \(\ell ^r\)-valued extension. We consider both non-atomic measures and measures with atoms and show the differences that can arise. We present some applications of our results to weighted norm inequalities of linear operators and vector-valued extensions of fractional operators with rough kernel.

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来源期刊
CiteScore
2.00
自引率
8.30%
发文量
67
审稿时长
>12 weeks
期刊介绍: The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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