Phi-Admissible singular operators and their commutators on vanishing generalized Orlicz-Morrey spaces

Abstract

We study the boundedness of Phi-admissible singular operators and their commutators on vanishing generalized Orlicz-Morrey spaces VM Phi,phi(R-n) including their weak versions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator, the Calder n-Zygmund singular integral operator and so on. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities on weights phi(x, r) without assuming any monotonicity property of phi(x, r) on r.