📝 SummarXiv

Abstract

A comprehensive description of Sobolev-type embeddings for generalized Lorentz-Zygmund spaces on bounded open subsets of the $n$-dimensional Euclidean space is offered. Rearrangement-invariant spaces, H\"older, Morrey and Campanato type spaces are the classes of range spaces taken into account. Within each of these classes, the optimal target spaces in the relevant embeddings are identified and discussed. This way neat explicit scenarios are developed, which seem to be still missing in the existing literature.