Abstract

In this paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals. Next, by employing these inequalities, we prove that the self-improving property (backward propagation property) of the weighted discrete Muckenhoupt classes holds. The main results give exact values of the limit exponents as well as the new constants of the new classes. As an application, we establish the self-improving property (forward propagation property) of the discrete Gehring class.

Details

Title
On discrete weighted Hardy type inequalities and properties of weighted discrete Muckenhoupt classes
Author
Saker, S H 1 ; Rabie, S S 1   VIAFID ORCID Logo  ; Agarwal, R P 2 

1  Mansoura University, Department of Mathematics, Faculty of Science, Mansoura, Egypt (GRID:grid.10251.37) (ISNI:0000000103426662); New Mansoura University, Department of Mathematics, Faculty of Science, New Mansoura City, Egypt (GRID:grid.10251.37) (ISNI:0000000103426662) 
2  Texas A&M University-Kingsvilie, Department of Mathematics, Texas, USA (GRID:grid.264756.4) (ISNI:0000 0004 4687 2082) 
Publication year
2021
Publication date
Dec 2021
Publisher
Springer Nature B.V.
ISSN
10255834
e-ISSN
1029242X
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1186/s13660-021-02702-y
ProQuest document ID
2582906188
Copyright
© The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.