Fractional sublinear operators with rough kernels and their commutators on new vanishing generalized Morrey spaces

Abstract

This study focuses on a class of fractional sublinear operators, denoted as S_Ω,α, and their commutators S_Ω,α,b with rough kernels. We establish the boundedness of these operators on newly emerging vanishing generalized Morrey spaces that are characterized by (V_∞) or (V^∗). The primary innovation of this paper lies in the novel approach of controlling S_Ω,α via the Riesz potential I_α and the management of S_Ω,α,b through fractional maximal commutators with rough kernels M_Ω,α−ε,b and M_Ω,α+ε,b for some ε > 0.

Keywords

Morrey space / vanishing properties / fractional integral / commutators / rough kernel / Mathematics Subject Classification: 47B34, 47B38

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