Boundedness of operators and inequalities on Morrey–Banach spaces

This paper establishes the boundedness of the spherical maximal function, Rubio de Fran-cia operators, Bochner–Riesz operators, Fourier integral operators, geometric maximal operator, minimal operator and strongly singular integral operators on Morrey spaces built on Banach function spaces. We also establish the Coifman–Fefferman inequalities, Gundy–Wheeden inequalities and Sobolev–Lieb–Thirring inequalities on Morrey–Banach spaces. In particular, our results include the boundedness of the above operators and inequalities on classical Morrey spaces, generalized Morrey spaces, Orlicz–Morrey spaces, Morrey–Lorentz spaces and Morrey spaces with variable exponents. Copyright © 2022 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.