Sobolev’s inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space Lp(·)(log L)q(·)

Our aim in this paper is to deal with Sobolev’s inequalities for Riesz potentials of functions belonging to Lp(·)(log L)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.