Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

In this paper, we give a boundedness criterion for the potential operator I-a in the local generalized Morrey space LMp,phi(t(0))(Gamma) and the generalized Morrey space M-p,M-phi(Gamma) defined on Carleson curves Gamma, respectively. For the operator I-a, we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on LMp,phi(t(0))(Gamma) and the strong and weak Adams-type boundedness on M-p,M-phi(Gamma).