Properties of Muckenhoupt and Gehring classes via conformable calculus

Volume 29, Issue 3, pp 203--213 https://doi.org/10.22436/jmcs.029.03.01

Publication Date: October 20, 2022 Submission Date: June 07, 2022 Revision Date: July 07, 2022 Accteptance Date: July 29, 2022

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Authors

S. H. Saker - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. - Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura City, Egypt. M. A. Darwish - Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt. H. A. Elshamy - Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.

Abstract

In this paper, we study the relationship between the Muckenhoupt class \(\mathcal{A}_{1}^{\alpha }(\mathcal{C})\) and the Gehring class \(\mathcal{G}% _{q}^{\alpha }(\mathcal{K})\) via conformable calculus. We also establish the constants of the classes for the power law functions.

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Keywords

• Conformable Muckenhoupt class
• conformable Gehring class
• Holder's inequality
• reverse Holder's inequality

MSC

•  40D05
•  40D25
•  42C10
•  43A55
•  46A35
•  46B15

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