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–Hormander type Fourier multipliers, and one on the constant in the triangle inequality for the spaces $$L^{p,r} $$ when $$p<1$$ .