Geodesic
Some notes on embedding for anisotropic Sobolev spaces
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 97-111
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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.
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.
DOI : 10.1007/s10587-011-0020-3
Classification : 42B35, 46E35
Keywords: Lorentz spaces; Sobolev spaces; Besov spaces; Sobolev embedding; rearrangement invariant spaces 
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Li, Hongliang; Sun, Quinxiu. Some notes on embedding for anisotropic Sobolev spaces. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 97-111. doi: 10.1007/s10587-011-0020-3

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