Hausdorff operators on homogeneous spaces of locally compact groups

A. Mirotin
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引用次数: 4

Abstract

Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.
局部紧群齐次空间上的Hausdorff算子
实线和多维欧几里德空间上的豪斯多夫算子起源于一些经典的求和方法。现在这是一个活跃的研究领域。作者自2019年开始定义并研究一般群上的Hausdorff算子。本文的目的是定义和研究局部紧群齐次空间上Lebesgue和real Hardy空间上的Hausdorff算子。我们特别地在局部紧群的齐次空间上引入了一个原子Hardy空间,并得到了这种空间上Hausdorff算子的有界性的条件。考虑了几个推论,并提出了尚未解决的问题。
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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