极大算子的交换子在 Morrey 空间的有界性以及对 Lipschitz 空间的刻画

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极大算子的交换子在 Morrey 空间的有界性以及对 Lipschitz 空间的刻画
Boundedness of the Commutators of the Maximal Operator on Morrey Spaces and Their Characterization of Lipschitz Spaces

DOI: 10.12677/PM.2023.1312366, PDF, 下载: 52 浏览: 102 科研立项经费支持
作者: 樊迪：牡丹江师范学院，数学科学学院，黑龙江牡丹江
关键词: Hardy-Littlewood 极大算子；Sharp 极大算子；交换子；Lipschitz 空间；Morrey 空间；Hardy-Littlewood Maximal Operator； Sharp Maximal Operator； Commutator； Lipschitz Space； Morrey Space

摘要: 设M为Hardy-Littlewood 极大算子，M^#为sharp 极大算子，b是局部可积函数。本文考虑了当b属于 Lipschitz 空间时，M 和M^#与b生成的极大交换子和非线性交换子在 Morrey 空间中的有界性，并给出了 Lipschitz 空间的一些新等价刻画。

Abstract: Let M be the Hardy-Littlewood maximal operator, M^# be the sharp maximal operator and b be a locally integrable function. In this paper, we consider the boundedness of maximal and nonlinear commutators generated by M and M^# with b on Morrey spaces when b belongs to the Lipschitz spaces, by which some new characterizations of the Lipschitz spaces are given.

文章引用：樊迪. 极大算子的交换子在 Morrey 空间的有界性以及对 Lipschitz 空间的刻画[J]. 理论数学, 2023, 13(12): 3514-3524. https://doi.org/10.12677/PM.2023.1312366

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