On embeddings of logarithmic Bessel potential spaces

Abstract

We present embedding theorems for certain logarithmic Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces and clarify the role of the logarithmic terms involved in the norms of the space mentioned. In particular, we get refinements of the Sobolev embedding theorems, Trudinger's limiting embedding as well as embeddings of Sobolev spaces into space ofλ-Hölder-continuous functions including the result of Brézis and Wainger. © 1997 Academic Press.