Fractional Operators on Morrey—Lorentz Spaces and the Olsen Inequality

Abstract

Under the Morrey norm, the fractional integral operator and the fractional maximal operator behave similarly as was initially proved by Adams and Xiao. Later on, Tanaka extended this result. The goal of this note is to extend their results on Morrey–Lorentz norm for exponents of full range. A passage to the vector-valued setting is done. Moreover, an Olsen-type inequality is obtained.