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    Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces
    (Tbilisi Centre Math Sci, 2020) Armutcu, Hatice; Eroglu, Ahmet; Isayev, Fatai
    In this paper we study the fractional maximal operator M-alpha in the local generalized Morrey space LMp,phi{to}(Gamma) and the generalized Morrey space M-p,M-phi(Gamma) defined on Carleson curves Gamma, respectively. For the operator M-alpha we shall give a characterization the strong and weak Spanne-Guliyev type boundedness on LMp,phi{to} (Gamma) and the strong and weak Adams-Guliyev type boundedness on M-p,M-phi(Gamma).