Orlicz-Morrey空间上Hardy-Littlewood极大算子和Calderón-Zygmund算子的加权有界性

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2021-08-16 DOI:10.7153/mia-2021-24-81

Ryota Kawasumi, E. Nakai

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引用次数: 1

摘要

对于Zygmund算子上的Hardy-Littlewood极大算子和Calder´算子，Lebesgue空间上的加权有界性是众所周知的。我们将这些扩展到奥利奇·莫里空间。此外，我们还证明了弱Orlicz-Morrey空间上的加权有界性。为此，我们给出了弱-弱模不等式。Orlicz-Morrey空间及其弱版本包含加权的Orlicz、Morrey和Lebesgue空间及其弱版作为特例。然后我们也得到了这些函数空间作为推论的有界性。

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Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces

For the Hardy-Littlewood maximal and Calder´on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak Orlicz-Morrey spaces. To do this we show the weak-weak modular inequality. The Orlicz-Morrey space and its weak version contain weighted Orlicz, Morrey and Lebesgue spaces and their weak versions as special cases. Then we also get the boundedness for these function spaces as corollaries.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.