Definability of singular integral operators on Morrey–Banach spaces

Abstract

We give a definition of singular integral operators on Morrey–Banach spaces which include Orlicz–Morrey spaces and Morrey spaces with variable exponents. The main result of this paper ensures that the singular integral operator is well-defined on the Morrey–Banach spaces. Therefore, it provides a solid foundation for the study of singular integral operators on Morrey type spaces. As an application of our main result, we study commutators of singular integral operators on Morrey–Banach spaces.