Riesz-type calculus for Lorentz-Morrey spaces

Abstract

This paper is devoted to a highly nontrivial study of $(0,n]\ni \alpha$-order Fourier transform-based Riesz integral-differential calculus for Lorentz-Morrey spaces (covering Lebesgue spaces): (i) Riesz integral traces of Lorentz-Morrey spaces; (ii) Riesz differential equations in dual Lorentz-Morrey spaces; (iii) Riesz variational capacities for Lorentz-Morrey spaces.