Title: Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent
Abstract: In this paper, we consider the Herz-Morrey space H p(•),q,ω {x0}and set(G).Our first aim in this paper is to give the boundedness of the maximal and Riesz potential operators in H p(•),q,ω (G) when q = ∞.In connection with H p(•),q,ω {x0}(G) and H p(•),q,ω (G), let us consider the families H(G) and Hp(•),q,ω (G).Following Fiorenza-Rakotoson [18], Di Fratta-Fiorenza [17] and Gogatishvili-Mustafayev [19], we next discuss the duality properties among these Herz-Morrey spaces.