A characterization for B-singular integral operator and its commutators on generalized weighted B-Morrey spaces

Abstract

We study the maximal operator M? and the singular integral operator A?, associated with the generalized shift operator. The generalized shift operators are associated with the Laplace-Bessel differential operator. Our analysis is based on two weighted inequalities for the maximal operator, singular integral operators, and their commutators, related to the Laplace-Bessel differential operator in generalized weighted B-Morrey spaces. Key words and phrases: B-maximal operator, B-singular integral operator, commutator, generalized weighted B-Morrey space.