Optimal domain spaces in Orlicz-Sobolev embeddings

Abstract

We deal with Orlicz-Sobolev embeddings in open subsets of ${\mathbb{R}}^n$. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces with respect to a Frostman measure, and, in particular, for trace embeddings on the boundary.

27 pages

References in corpus (1)

• Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces

Cited by in corpus (4)

• Boundedness of classical operators on rearrangement-invariant spaces
• Embeddings of homogeneous Sobolev spaces on the entire space
• Fractional Maximal Operator in Orlicz spaces
• On the properties of rearrangement-invariant quasi-Banach function spaces