Embeddings for spaces of Lorentz-Sobolev type

Abstract

The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation between classes of endpoint Mikhlin-H\"ormander type Fourier multipliers, and one on the constant in the triangle inequality for the spaces $L^{p,r} $ when $p<1$.