Some notes on embedding for anisotropic Sobolev spaces

Hongliang Li; Quinxiu Sun

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 97-111
  • ISSN: 0011-4642

Abstract

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In this paper, we prove new embedding theorems for generalized anisotropic Sobolev spaces, W Λ p , q ( w ) r 1 , ⋯ , r n and W X r 1 , ⋯ , r n , where Λ p , q ( w ) is the weighted Lorentz space and X is a rearrangement invariant space in ℝ n . The main methods used in the paper are based on some estimates of nonincreasing rearrangements and the applications of B p weights.

How to cite

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Li, Hongliang, and Sun, Quinxiu. "Some notes on embedding for anisotropic Sobolev spaces." Czechoslovak Mathematical Journal 61.1 (2011): 97-111. <http://eudml.org/doc/196962>.

@article{Li2011,
abstract = {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.},
author = {Li, Hongliang, Sun, Quinxiu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lorentz spaces; Sobolev spaces; Besov spaces; Sobolev embedding; rearrangement invariant spaces; Lorentz space; Sobolev space; Besov space; Sobolev embedding; rearrangement invariant space},
language = {eng},
number = {1},
pages = {97-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some notes on embedding for anisotropic Sobolev spaces},
url = {http://eudml.org/doc/196962},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Li, Hongliang
AU - Sun, Quinxiu
TI - Some notes on embedding for anisotropic Sobolev spaces
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 97
EP - 111
AB - 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.
LA - eng
KW - Lorentz spaces; Sobolev spaces; Besov spaces; Sobolev embedding; rearrangement invariant spaces; Lorentz space; Sobolev space; Besov space; Sobolev embedding; rearrangement invariant space
UR - http://eudml.org/doc/196962
ER -

References

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