Sharp weak bounds for discrete Hardy operator on discrete central Morrey spaces

Mingquan Wei; Xiaoyu Liu; Mingquan Wei; Xiaoyu Liu

doi:10.3934/math.2023250

AIMS Mathematics

2023, Volume 8, Issue 2: 5007-5015. doi: 10.3934/math.2023250

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Research article

Sharp weak bounds for discrete Hardy operator on discrete central Morrey spaces

Mingquan Wei ^,,
Xiaoyu Liu

School of Mathematics and Stastics, Xinyang Normal University, Xinyang, Henan 464000, China

Received: 09 September 2022 Revised: 19 November 2022 Accepted: 01 December 2022 Published: 12 December 2022
MSC : 42B20, 42B25, 42B35

In this note, we introduce the discrete (weak) central Morrey spaces, which are central versions of discrete (weak) Morrey spaces. The sharp bounds for discrete Hardy operator from discrete central Morrey spaces to discrete weak central Morrey spaces are proven to be equal to 1. As an application, we obtain the weak version of the well-known discrete Hardy inequality.
- discrete Hardy operator,
- sharp bound,
- discrete central Morrey space,
- discrete Lebesgue space
Citation: Mingquan Wei, Xiaoyu Liu. Sharp weak bounds for discrete Hardy operator on discrete central Morrey spaces[J]. AIMS Mathematics, 2023, 8(2): 5007-5015. doi: 10.3934/math.2023250

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Abstract

In this note, we introduce the discrete (weak) central Morrey spaces, which are central versions of discrete (weak) Morrey spaces. The sharp bounds for discrete Hardy operator from discrete central Morrey spaces to discrete weak central Morrey spaces are proven to be equal to 1. As an application, we obtain the weak version of the well-known discrete Hardy inequality.

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