RIESZ TRANSFORMS ASSOCIATED WITH SCHRODINGER OPERATOR ON VANISHING GENERALIZED MORREY SPACES

Abstract

In this paper, we study the boundedness of the dual Riesz transform R* and their commutators [b, R*] on generalized Morrey spaces M-p,phi(alpha,V) associated with Schrodinger operator and vanishing generalized Morrey spaces V M-p,phi(alpha,V) associated with Schrodinger operator. We find the sufficient conditions on the pair (phi(1) , phi(2)) which ensures the boundedness of the operator R* from one vanishing generalized Morrey space V M-p,phi 1(alpha,V) to another V M-p,phi 2(alpha,V).