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Research Article | Open Access

Novel insights into the precise boundedness and Lipschitz continuity of Hardy-type operators within central Morrey spaces

Muhammad Asim1( ), Ghada AlNemer2
Department of NUSASH, National University of Technology (NUTECH), Islamabad 44000, Pakistan
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
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Abstract

In this study, precise evaluations of the optimal constants associated with weighted weak-type Hardy inequalities are established. The analysis extends to the computation of the weak-type operator norm of the fractional Hardy operator within the framework of weighted central Morrey spaces. Furthermore, it is demonstrated that the commutators of the Hardy operator exhibit boundedness on these weighted central Morrey spaces when the symbol functions reside in the weighted Lipschitz space.

Keywords

Hardy-type operatorssharp constantsLipschitz spaceweights
CLC number: 42B35, 26D10, 47B38, 47G10

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AIMS Mathematics
Volume 10 Issue 10,
October 2025
Pages 23547-23563
DOI: 10.3934/math.20251046

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Cite this article:
Asim M, AlNemer G. Novel insights into the precise boundedness and Lipschitz continuity of Hardy-type operators within central Morrey spaces. AIMS Mathematics, 2025, 10(10): 23547-23563. https://doi.org/10.3934/math.20251046

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Received: 04 July 2025
Revised: 19 September 2025
Accepted: 25 September 2025
Published: 16 October 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)