Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(⋅)(logL)q(⋅)

Our aim in this paper is to deal with Sobolev's inequalities for Riesz potentials of functions belonging to Lp(⋅)(logL)q(⋅). To do so, we study the boundedness of Hardy–Littlewood maximal functions and apply the Hedberg's trick. As an application, we treat vanishing integrability for Riesz potentials.