Small Lebesgue spaces and their applications
The authors' present some properties and applications of the so-called small Lebesgue spaces. These spaces share some common properties with the usual Lebesgue spaces as the monotone Levi properties. However, there are some properties which are true for the normal Lebesgue spaces and not satisfied by so-called small Lebesgue ones. As for the application of the monotone Levi property, and the pointwise Poincaré-Sobolev inequality, the authors' derive some new and precises estimates either for small Lebesgue-Sobolev spaces or for quasilinear equations with data in the small Lebesgue spaces.
scientific article; zbMATH DE number 1744394