Sharpness and non-compactness of embeddings of Bessel-potential-type spaces

Abstract

We establish embeddings for Bessel potential spaces modeled upon Lorentz-Karamata spaces with order of smoothness less than one. The target spaces are of Hölder-continuous type. In the super-limiting case we also prove that the embedding is sharp and fails to be compact. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)