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Volume 14
Issue 12
10.3390/axioms14120894
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Article

Generalized Local Morrey Spaces Associated with Ball Banach Function Spaces and Their Application

by
Feiyang Zhang
and
Jiang Zhou
*
College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(12), 894; https://doi.org/10.3390/axioms14120894 (registering DOI)
Submission received: 28 October 2025 / Revised: 27 November 2025 / Accepted: 1 December 2025 / Published: 1 December 2025
(This article belongs to the Special Issue Applications in Harmonic Analysis)
Versions Notes

Abstract

This paper is devoted to the analysis of boundedness for fractional integral operators, Calderón–Zygmund singular integral operators, and their corresponding commutators on generalized local Morrey spaces associated with ball Banach function spaces. These foundational results are then applied to establish the local regularity within the LMXφ Morrey spaces for the solution gradients of second-order elliptic equations expressed in divergence form.
Keywords: generalized local Morrey spaces; ball Banach function spaces; regularity; commutators generalized local Morrey spaces; ball Banach function spaces; regularity; commutators

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MDPI and ACS Style

Zhang, F.; Zhou, J. Generalized Local Morrey Spaces Associated with Ball Banach Function Spaces and Their Application. Axioms 2025, 14, 894. https://doi.org/10.3390/axioms14120894

AMA Style

Zhang F, Zhou J. Generalized Local Morrey Spaces Associated with Ball Banach Function Spaces and Their Application. Axioms. 2025; 14(12):894. https://doi.org/10.3390/axioms14120894

Chicago/Turabian Style

Zhang, Feiyang, and Jiang Zhou. 2025. "Generalized Local Morrey Spaces Associated with Ball Banach Function Spaces and Their Application" Axioms 14, no. 12: 894. https://doi.org/10.3390/axioms14120894

APA Style

Zhang, F., & Zhou, J. (2025). Generalized Local Morrey Spaces Associated with Ball Banach Function Spaces and Their Application. Axioms, 14(12), 894. https://doi.org/10.3390/axioms14120894

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