Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent

Our aim in this paper is to deal with Sobolev embeddings for Riesz potentials of order α for functions f satisfying the Orlicz type condition∫|f(y)|p(y)(log(c+|f(y)|))q(y)dy<∞, where p(⋅)p(⋅) and q(⋅)q(⋅) are variable exponents satisfying the log-Hölder conditions.