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

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.