Potential Operator on Carleson Curves in Local Generalized Weighted Morrey Spaces

Abstract

In this paper we give a strong and weak type Guliyev-Spanne type boundedness criterion for the potential operator I alpha in the local generalized weighted Morrey space p,phi (Gamma, w) and the generalized weighted Morrey space Mp,phi(Gamma, w) defined on Carleson curves Gamma. For the operator I alpha we establish necessary and sufficient conditions for the p,phi (Gamma, w) and the strong and weak Guliyev-Spanne type boundedness and Mp,phi(Gamma, w).