CHOQUET INTEGRALS, HAUSDORFF CONTENT AND FRACTIONAL OPERATORS

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-03-19 DOI:10.1017/s000497272400011x

NAOYA HATANO, RYOTA KAWASUMI, HIROKI SAITO, HITOSHI TANAKA

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引用次数: 0

Abstract

We show that the fractional integral operator

$I_{\alpha }$

$0<\alpha <n$

, and the fractional maximal operator

$M_{\alpha }$

$0\le \alpha <n$

, are bounded on weak Choquet spaces with respect to Hausdorff content. We also investigate these operators on Choquet–Morrey spaces. The results for the fractional maximal operator

$M_\alpha $

are extensions of the work of Tang [‘Choquet integrals, weighted Hausdorff content and maximal operators’, Georgian Math. J.18(3) (2011), 587–596] and earlier work of Adams and Orobitg and Verdera. The results for the fractional integral operator

$I_{\alpha }$

are essentially new.

查看原文本刊更多论文

choquet 积分、hausdorff 内容和分式算子

我们证明了分数积分算子 $I_{\alpha }$ , $0<\alpha <n$ 和分数最大算子 $M_{\alpha }$ , $0\le \alpha <n$ 在弱 Choquet 空间上关于 Hausdorff 内容是有界的。我们还在 Choquet-Morrey 空间上研究了这些算子。小数最大算子 $M_\alpha $ 的结果是唐['Choquet 积分、加权 Hausdorff 内容和最大算子'，Georgian Math.J.18（3）（2011），587-596] 以及亚当斯和奥罗比特及韦尔德拉的早期工作。分数积分算子 $I_{\alpha }$ 的结果本质上是新的。

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

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society