MARCINKIEWICZ INTEGRALS ASSOCIATED WITH SCHRODINGER OPERATOR ON GENERALIZED MORREY SPACES

Abstract

Let L = -Delta+V be a Schrodinger operator, where. is the Laplacian on R-n, while nonnegative potential V belongs to the reverse Holder class. In this paper, we study the boundedness of the Marcinkiewicz operator associated with Schrodinger operator mu(L)(j) on generalized Morrey spaces M-p,M-phi. We find the sufficient conditions on the pair (phi(1),phi(2)) which ensures the boundedness of the operators mu(L)(j) from one generalized Morrey space M-p,M-phi 1 to another M-p,M-phi 2, 1 < p < infinity and from the space M-1,M-phi 1 to the weak space WM1,phi 2.