Lorentz-Karamata spaces, Bessel and Riesz potentials and embeddings
We consider Lorentz-Karamata spaces and establish embedding theorems (some local and some global) for Bessel-potential spaces modelled upon appropriate Lorentz-Karamata spaces into Lorentz-Karamata spaces and Orlicz spaces. In particular, we obtain refinements of the Sobolev embedding theorems: Strichartz-Trudinger's limiting case and Hansson-Brézis-Wainger's limiting case. These results extend and improve those of Edmunds, Gurka and Opic. Estimates for an appropriate norm of the convolution of...