Self-improving properties of discrete Muckenhoupt weights

Ravi P. Agarwal; Samir H. Saker; Donal O'Regan

doi:10.1515/anly-2020-0052

Self-improving properties of discrete Muckenhoupt weights

Ravi P. Agarwal, Samir H. Saker, Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we will provide a complete study of the self-improving properties of the discrete Muckenhoupt class p of weights defined on +{\mathbb{Z}-{+}}. In addition, we will determine the range of the new constants which are related to the original constants via an algebraic equation. For illustration, we will give an example to prove that the results are sharp. The results will be obtained by employing a discrete version of an inequality due to Hardy-Littlewood and a new discrete Hardy-Type inequality with negative powers.

Original language	English
Pages (from-to)	169-178
Number of pages	10
Journal	Analysis (Germany)
Volume	41
Issue number	3
DOIs	https://doi.org/10.1515/anly-2020-0052
Publication status	Published - 1 Aug 2021

Keywords

discrete Muckenhoupt class
Hardy-Type inequality
higher summability
self-improving properties

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10.1515/anly-2020-0052

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abstract = "In this paper, we will provide a complete study of the self-improving properties of the discrete Muckenhoupt class p of weights defined on +{\mathbb{Z}-{+}}. In addition, we will determine the range of the new constants which are related to the original constants via an algebraic equation. For illustration, we will give an example to prove that the results are sharp. The results will be obtained by employing a discrete version of an inequality due to Hardy-Littlewood and a new discrete Hardy-Type inequality with negative powers.",

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author = "Agarwal, {Ravi P.} and Saker, {Samir H.} and Donal O'Regan",

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AU - Saker, Samir H.

AU - O'Regan, Donal

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Y1 - 2021/8/1

N2 - In this paper, we will provide a complete study of the self-improving properties of the discrete Muckenhoupt class p of weights defined on +{\mathbb{Z}-{+}}. In addition, we will determine the range of the new constants which are related to the original constants via an algebraic equation. For illustration, we will give an example to prove that the results are sharp. The results will be obtained by employing a discrete version of an inequality due to Hardy-Littlewood and a new discrete Hardy-Type inequality with negative powers.

AB - In this paper, we will provide a complete study of the self-improving properties of the discrete Muckenhoupt class p of weights defined on +{\mathbb{Z}-{+}}. In addition, we will determine the range of the new constants which are related to the original constants via an algebraic equation. For illustration, we will give an example to prove that the results are sharp. The results will be obtained by employing a discrete version of an inequality due to Hardy-Littlewood and a new discrete Hardy-Type inequality with negative powers.

KW - discrete Muckenhoupt class

KW - Hardy-Type inequality

KW - higher summability

KW - self-improving properties

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Self-improving properties of discrete Muckenhoupt weights

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Keywords

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