Quantum \(L^p\)-spaces and inequalities of Hardy's type

Volume 31, Issue 3, pp 274--286 http://dx.doi.org/10.22436/jmcs.031.03.04

Publication Date: May 12, 2023 Submission Date: February 05, 2023 Revision Date: March 04, 2023 Accteptance Date: April 05, 2023

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Authors

A. E. Hamza - Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt. M. A. Alghamdi - Department of Mathematics, College of Science, University of Jeddah, Jeddah, 21589, Saudi Arabia. S. A. Alasmi - Department of Mathematics, College of Science, University of Jeddah, Jeddah, 21589, Saudi Arabia.

Abstract

In this paper, we revisit the \(L^p\)-spaces, \(p\geq 1\), associated with a general quantum difference operator and prove some convergence theorems in the quantum setting. Furthermore, two inequalities of Hardy's type are established. Finally, many illustrative examples concerning with \(q\)-difference operator, Hahn difference operator and power quantum difference operator are given.

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ISRP Style

A. E. Hamza, M. A. Alghamdi, S. A. Alasmi, Quantum \(L^p\)-spaces and inequalities of Hardy's type, Journal of Mathematics and Computer Science, 31 (2023), no. 3, 274--286

AMA Style

Hamza A. E., Alghamdi M. A., Alasmi S. A., Quantum \(L^p\)-spaces and inequalities of Hardy's type. J Math Comput SCI-JM. (2023); 31(3):274--286

Chicago/Turabian Style

Hamza, A. E., Alghamdi, M. A., Alasmi, S. A.. "Quantum \(L^p\)-spaces and inequalities of Hardy's type." Journal of Mathematics and Computer Science, 31, no. 3 (2023): 274--286

Keywords

Quantum difference operator
quantum calculus
Hahn difference operator
Jackson q-difference operator

MSC

39A10
39A70
39A13

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