On the boundedness of singular integral operators on grand variable Herz-Hardy spaces

Volume 40, Issue 4, pp 501--512 https://dx.doi.org/10.22436/jmcs.040.04.04

Publication Date: August 14, 2025 Submission Date: April 06, 2025 Revision Date: April 27, 2025 Accteptance Date: May 06, 2025

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Authors

B. Sultan - Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan. A. Hussain - Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan. N. M. Aloraini - Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia. I.-L. Popa - Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania. - Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania.

Abstract

This study investigates the boundedness of various commutators on grand variable Herz-Hardy spaces, including the Marcinkiewicz integral operator, the Calderón-Zygmund singular integral operator and the fractional integral operator. Firstly we define the Lebesgue spaces with variable exponent and some basic lemmas including Hölder's inequality for Lebesgue spaces. We use the definition of variable Herz spaces to give the definition of grand variable Herz spaces. Then we apply the atomic decomposition of grand variable Herz-Hardy spaces to obtain the boundedness of Marcinkiewicz integral operator, Calderón-Zygmund singular integral operator and fractional integral operator on grand variable Herz-Hardy spaces.

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Keywords

• Fractional integral operator
• Calderón-Zygmund singular integral operator
• mathematical operators
• grand variable Herz spaces
• grand Herz-Hardy spaces

MSC

•  46E35
•  42B25
•  42B35

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