GENERALIZED LOCAL WEIGHTED MORREY SPACES ON CARLESON CURVES AND FRACTIONAL MAXIMAL OPERATOR

Abstract

In the paper we study the fractional maximal operator M-Gamma,M-alpha defined on Carleson curves Gamma in the generalized local weighted LMp phi ({t)(0)} (Gamma omega) and the generalized weighted Morrey space M-p,M-phi (Gamma, omega), respectively. We give a strong and weak type Guliyev-Spanne type boundedness criterion for the fractional maximal operator M-Gamma,M-alpha in the generalized local weighted Morrey space LM0{t} (p,phi) (Gamma,omega) and the generalized weighted Morrey space M-p,M-phi (Gamma, omega) defined on Carleson curves F. For the operator M-Gamma,M-alpha, necessary and sufficient conditions for strong and weak boundedness of the Guliyev-Spanne type on LM0{t}(p,phi) (Gamma,omega) and the strong and weak Guliyev-Spanne type boundedness on M-p,M- phi (Gamma, omega) are established. We shall give characterizations the strong and weak Guliyev-Spanne type boundedness of the operator M-Gamma,M-alpha from LM0{x}(p,phi 1) (Gamma,omega) to LM0{x}(q,phi 2) (Gamma,omega) , 1 <= q