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Compactness for Sobolev-type trace operators. (English) Zbl 1426.46017

Summary: Compactness of arbitrary-order Sobolev type embeddings for traces of \(n\)-dimensional functions on lower dimensional subspaces is investigated. Sobolev spaces built upon any rearrangement-invariant norm are allowed. In particular, we characterize compactness of trace embeddings for classical Sobolev, Lorentz-Sobolev and Orlicz-Sobolev type spaces.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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