Abstract
We prove some new properties of the small Lebesgue spaces introduced by Fiorenza in [F]. Combining these properties with the Poincare-Sobolev inequalities for the relative rearrangement (see [R1]), we derive some new and precises estimates either for small Lebesgue-Sobolev spaces or for quasilinear equations with data in the small Lebesgue spaces.
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