On dimension-free Sobolev imbeddings. I. (English) Zbl 1238.46027
Several dimension-free invariant imbedding theorems for (weighted) Sobolev spaces are proved in this paper by using as a main tool the Gross logarithmic inequality. These results concern a bounded domain \(\Omega\) in \(\mathbb{R}^N\) or the whole space \(\mathbb{R}^N\). Special Orlicz spaces are used in the proofs.
Reviewer: Jesús Hernández (Madrid)
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.) |
Keywords:
dimension-free imbeddings; Sobolev spaces; weighted Sobolev spaces; Gross logarithmic inequality; special Orlicz spacesReferences:
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