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Our aim in this paper is to deal with 0-Holder continuity for Riesz potentials of functions belonging to Lebesgue’s Lp space of variable exponent, in the borderline case of Sobolev’s theorem. We are also concerned with exponential integrability for Riesz potentials.

Continuity properties of Riesz potentials for functions in L^p(⋅) of variable exponent