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Title: Some notes on embedding for anisotropic Sobolev spaces (English)
Author: Li, Hongliang
Author: Sun, Quinxiu
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 61
Issue: 1
Year: 2011
Pages: 97-111
Summary lang: English
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Category: math
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Summary: In this paper, we prove new embedding theorems for generalized anisotropic Sobolev spaces, $W_{\Lambda ^{p,q}(w)}^{r_1,\dots ,r_n}$ and $W_{X}^{r_1,\dots ,r_n}$, where $\Lambda ^{p,q}(w)$ is the weighted Lorentz space and $X$ is a rearrangement invariant space in $\mathbb R^n$. The main methods used in the paper are based on some estimates of nonincreasing rearrangements and the applications of $B_p$ weights. (English)
Keyword: Lorentz spaces
Keyword: Sobolev spaces
Keyword: Besov spaces
Keyword: Sobolev embedding
Keyword: rearrangement invariant spaces
MSC: 42B35
MSC: 46E35
idZBL: Zbl 1224.46065
idMR: MR2782762
DOI: 10.1007/s10587-011-0020-3
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Date available: 2011-05-23T12:34:27Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/141521
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