Some notes on embedding for anisotropic Sobolev spaces

Abstract

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