HIGHER ORDER RIESZ TRANSFORMS RELATED TO SCHRODINGER TYPE OPERATOR ON LOCAL GENERALIZED MORREY SPACES

Abstract

In this paper, we study the boundedness of the higher order Riesz transforms R, R* and their commutators [b, R], [b, R*] on local generalized Morrey spaces LMp,phi alpha,V,{x0} and vanishing generalized Morrey spaces VMp,phi alpha,V related to Schrodinger type operator. We find the sufficient conditions on the pair (phi(1),phi(2)) which ensures the boundedness of these operators from one local generalized Morrey space LMp,phi alpha,V,{x0} to another LMp,phi 2 alpha,V,{x0} and from one vanishing generalized Morrey space VMp,phi alpha,V to another VMp,phi 2 alpha,V.