## The weighted discrete Gehring classes, Muckenhoupt classes and their basic properties

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- by Samir H. Saker and Mario Krnić PDF
- Proc. Amer. Math. Soc.
**149**(2021), 231-243 Request permission

## Abstract:

The main objective of this paper is a study of the structure and basic properties of the weighted discrete Gehring classes, as well as the study of the relationship between discrete Muckenhoupt and Gehring classes. First, we prove that the weighted discrete Muckenhoupt class $\mathcal {A}_{\lambda }^{1}(C)$, $C>1$, consisting of nonincreasing sequences, belongs to the weighted discrete Gehring class $\mathcal {G}_{\lambda }^{p}(A)$ by giving explicit values of exponent $p$ and constant $A$. Next, we prove the self-improving property of the weighted Gehring class $\mathcal {G}_{\lambda }^{p}({K)}$, $p>1$, $K>1$, consisting of nonincreasing sequences. The exponent and constant of transition are explicitly given. Finally, utilizing the self-improving property of the weighted Gehring class, we also derive the self-improving property of a discrete Muckenhoupt class $\mathcal {A}^{p}(C)$, $p>1$, $C>1$, with exact values of exponent and constant of transition.## References

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## Additional Information

**Samir H. Saker**- Affiliation: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
- MR Author ID: 650100
- Email: shsaker@mans.edu.eg
**Mario Krnić**- Affiliation: University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
- Email: mario.krnic@fer.hr
- Received by editor(s): March 26, 2020
- Received by editor(s) in revised form: April 29, 2020
- Published electronically: October 9, 2020
- Communicated by: Mourad Ismail
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 231-243 - MSC (2010): Primary 40D05, 40D25; Secondary 42C10, 43A55, 46B15
- DOI: https://doi.org/10.1090/proc/15180
- MathSciNet review: 4172600