加权局部Morrey空间

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2020-01-01 DOI:10.5186/aasfm.2020.4504

Shohei Nakamura, Y. Sawano, Hitoshi Tanaka

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引用次数: 10

摘要

摘要讨论了两类加权局部Morrey空间中线性算子和次线性算子的有界性。其中一个是由Natasha Samko在2008年定义的。另一个是由小森古屋康夫和白井聪在2009年定义的。我们刻画了Hardy-Littlewood极大算子有界的一类权值。在一定的积分条件下，证明奇异积分算子当且仅当Hardy-Littlewood极大算子有界时是有界的。作为表征的一个应用，我们考虑幂权函数|·|。可以完整地描述α上Hardy-Littlewood极大算子有界的条件。

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Weighted local Morrey spaces

Abstract. We discuss the boundedness of linear and sublinear operators in two types of weighted local Morrey spaces. One is defined by Natasha Samko in 2008. The other is defined by Yasuo Komori-Furuya and Satoru Shirai in 2009. We characterize the class of weights for which the Hardy–Littlewood maximal operator is bounded. Under a certain integral condition it turns out that the singular integral operators are bounded if and only if the Hardy–Littlewood maximal operator is bounded. As an application of the characterization, the power weight function | · | is considered. The condition on α for which the Hardy–Littlewood maximal operator is bounded can be described completely.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.