Parametric Marcinkiewicz integral operator on generalized Orlicz-Morrey spaces

Abstract

In this paper we study the boundedness of the parametric Marcinkiewicz integral operator µ? ? on generalized Orlicz-Morrey spaces M?,?;'. We find the sufficient conditions on the pair (?1; ?'2;?) which ensure the boundedness of the operators µ?,? from one generalized Orlicz-Morrey space M?;?1 to another M?,?2. As an application of the above result, the boundedness of the Marcinkiewicz operator associated with Schrödinger operator µL j on generalized Orlicz-Morrey spaces is also obtained. © 2016, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.