Hausdorff operators on homogeneous spaces of locally compact groups

DOI: https://doi.org/10.33581/2520-6508-2020-2-28-35

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.

Author Biography

Adolf R. Mirotin, Francisk Skorina Gomel State University, 104 Savieckaja Street, Homieĺ 246019, Belarus

doctor of science (physics and mathematics), full professor; head of the department of mathematical analysis and differential equations, faculty of mathematics and technologies of programming

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Published
2020-07-30
Keywords: Hausdorff operator, locally compact group, homogeneous space, atomic Hardy space, Lebesgue space, bounded operator
How to Cite
Mirotin, A. R. (2020). Hausdorff operators on homogeneous spaces of locally compact groups. Journal of the Belarusian State University. Mathematics and Informatics, 2, 28-35. https://doi.org/10.33581/2520-6508-2020-2-28-35
Issue
No 2 (2020): Journal of the Belarusian State University. Mathematics and Informatics
Section
Real, Complex and Functional Analysis

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