Conformable Gehring inequalities and conformable higher integrability

Volume 29, Issue 2, pp 192--202 https://doi.org/10.22436/jmcs.029.02.08

Publication Date: October 20, 2022 Submission Date: June 07, 2022 Revision Date: July 17, 2022 Accteptance Date: July 21, 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 prove some reverse conformable inequalities with weights and employ them to prove some conformable inequalities of Gehring type. Moreover, we prove some interpolation theorems which are powerful tools in\ the study of operators in function spaces. Our results develop a technique based on the applications of a refinement of conformable inequalities.

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Keywords

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

MSC

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

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