Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Abstract

We introduce a new type of variable exponent function spaces \(M\dot K_{q,p( \cdot )}^{\alpha ( \cdot ),\lambda } (\mathbb{R}^n )\) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderon-Zygmund operators and their commutators of BMO function on these Morrey-Herz type spaces by applying the properties of variable exponent and BMO norms.