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Mathematics
Volume 14
Issue 10
10.3390/math14101713
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Article

Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces

by
Muhammad Asim
1 and
Ghada AlNemer
2,*
1
Department of NUSASH, National University of Technology (NUTECH), Islamabad 44000, Pakistan
2
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(10), 1713; https://doi.org/10.3390/math14101713 (registering DOI)
Submission received: 15 April 2026 / Revised: 4 May 2026 / Accepted: 10 May 2026 / Published: 16 May 2026
(This article belongs to the Special Issue Mathematical Inequalities and Fractional Calculus)
Versions Notes

Abstract

Within the present scholarly exposition, a meticulous and rigorous analysis is undertaken to investigate the boundedness characteristics of rough Hardy operators in the refined structural setting of variable exponent Morrey–Herz spaces. Moreover, parallel and quantitatively precise estimates are systematically established for the associated commutator operators, under the fundamental premise that the underlying symbol functions reside in the variable exponent bounded mean oscillation space (BMO).
Keywords: rough Hardy operator; BMO; boundedness inequalities; function spaces rough Hardy operator; BMO; boundedness inequalities; function spaces

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MDPI and ACS Style

Asim, M.; AlNemer, G. Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces. Mathematics 2026, 14, 1713. https://doi.org/10.3390/math14101713

AMA Style

Asim M, AlNemer G. Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces. Mathematics. 2026; 14(10):1713. https://doi.org/10.3390/math14101713

Chicago/Turabian Style

Asim, Muhammad, and Ghada AlNemer. 2026. "Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces" Mathematics 14, no. 10: 1713. https://doi.org/10.3390/math14101713

APA Style

Asim, M., & AlNemer, G. (2026). Boundedness Results and Commutator Inequalities for Rough Hardy Operators on Variable Exponent Morrey–Herz Spaces. Mathematics, 14(10), 1713. https://doi.org/10.3390/math14101713

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