Sobolev embeddings in Orlicz and Lorentz spaces with measures

Abstract

Embedding theorems for Orlicz-Sobolev spaces into Orlicz or Orlicz-Lorentz spaces in domains in R-n, endowed with a Frostman measure, are offered. Parallel embeddings for Lorentz-Sobolev spaces into (generalized) Lorentz spaces are also established.

The relevant embeddings yield an optimal target norm, in the relevant classes, whenever it does exist. In particular, various results available in the literature are improved by special choices of the function spaces and of the measure. (C) 2020 Elsevier Inc.

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Keywords

• Frostman measures
• Orlicz-Sobolev spaces
• Lorentz-Sobolev spaces
• Sobolev trace embeddings
• Higher-order derivatives