Some notes on embedding for anisotropic Sobolev spaces

Li, Hongliang ; Sun, Quinxiu

Czechoslovak Mathematical Journal, Tome 61 (2011) no. 1, pp. 97-111.

Résumé

In this paper, we prove new embedding theorems for generalized anisotropic Sobolev spaces, $W_{{\mathrm{\Lambda }}^{p,q}(w)}^{r_1,\dots ,r_n}$ and $W_X^{r_1,\dots ,r_n}$, where ${\mathrm{\Lambda }}^{p,q}(w)$ 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.

Détail

DOI : 10.1007/s10587-011-0020-3

Classification : 42B35, 46E35
Mots-clés : Lorentz spaces; Sobolev spaces; Besov spaces; Sobolev embedding; rearrangement invariant spaces