On dimension-free Sobolev imbeddings. I. (Q645373)
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scientific article; zbMATH DE number 5971760
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| English | On dimension-free Sobolev imbeddings. I. |
scientific article; zbMATH DE number 5971760 |
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On dimension-free Sobolev imbeddings. I. (English)
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15 November 2011
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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.
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dimension-free imbeddings
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Sobolev spaces
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weighted Sobolev spaces
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Gross logarithmic inequality
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special Orlicz spaces
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