Estimates for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand variable Herz-Morrey spaces

Jiayue Liu; Liqiong Duan; Jie Sun; Jiayue Liu; Liqiong Duan; Jie Sun

doi:10.3934/era.2026269

Electronic Research Archive

2026, Volume 34, Issue 9: 6101-6120. doi: 10.3934/era.2026269

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Research article

Estimates for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand variable Herz-Morrey spaces

Department of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China

Received: 09 April 2026 Revised: 21 June 2026 Accepted: 09 July 2026 Published: 15 July 2026

The aim of this paper was to discuss the boundedness of commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand Herz-Morrey spaces with two variable exponents $ \eta(\cdot), \; q(\cdot) $. We proved that the fractional Hardy and Hardy-Littlewood-Pólya operators are bounded on grand variable Herz-Morrey spaces, where the symbols of the commutators belong to Lipschitz spaces.
- Hardy-Littlewood-Pólya operator,
- fractional Hardy-type operator,
- variable exponent Herz-Morrey space,
- commutator
Citation: Jiayue Liu, Liqiong Duan, Jie Sun. Estimates for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand variable Herz-Morrey spaces[J]. Electronic Research Archive, 2026, 34(9): 6101-6120. doi: 10.3934/era.2026269

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Abstract

The aim of this paper was to discuss the boundedness of commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand Herz-Morrey spaces with two variable exponents $ \eta(\cdot), \; q(\cdot) $. We proved that the fractional Hardy and Hardy-Littlewood-Pólya operators are bounded on grand variable Herz-Morrey spaces, where the symbols of the commutators belong to Lipschitz spaces.

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