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 LMα,V,{x0} p,φ and vanishing generalized Morrey spaces VMα,V p,φ related to Schr¨odinger type operator. We find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of these operators from one local generalized Morrey space LMα,V,{x0} p,φ to another LMα,V,{x0} p,φ2 and from one vanishing generalized Morrey space VMα,V p,φ to another VMα,V p,φ2 .

Keywords:

Schrodinger type operator, higher order Riesz transform, commutator, BMO, local generalized Morrey space