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 the commutators of singular integral operators on Morrey-Banach spaces. Copyright © 2018 the Mathematical Society of Japan.
CitationHo, K.-P. (2020). Definability of singular integral operators on Morrey-Banach spaces. Journal of the Mathematical Society of Japan, 72(1), 155-170. doi: 10.2969/jmsj/81208120
- Singular integral operator
- Morrey space
- Banach function space
- Variable exponent analysis