Characterization of Lipschitz functions via the commutators of multilinear fractional integral operators in variable Lebesgue spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2023-01-01 DOI:10.1515/agms-2022-0153

Pu Zhang, Jiang-Long Wu

引用次数: 0

Abstract

Abstract The main purpose of this article is to establish some new characterizations of the (variable) Lipschitz spaces in terms of the boundedness of commutator of multilinear fractional Calderón-Zygmund integral operators in the context of the variable exponent Lebesgue spaces. The authors do so by applying the techniques of Fourier series and multilinear fractional integral operator, as well as some pointwise estimates for the commutators. The key tool in obtaining such a pointwise estimate is a certain generalization of the classical sharp maximal operator.

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通过变Lebesgue空间中多线性分数积分算子的交换子刻画Lipschitz函数

摘要本文的主要目的是在变指数Lebesgue空间中，根据多重线性分式Calderón-Zygmund积分算子的交换子的有界性，建立（可变）Lipschitz空间的一些新的刻画。作者通过应用傅立叶级数和多线性分数积分算子的技术，以及对交换子的一些逐点估计来做到这一点。获得这种逐点估计的关键工具是对经典sharp极大算子的某种推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.