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 Λp,q(w) is the weighted Lorentz space and X is a rearrangement invariant space in ℝn. The main methods used in the paper are based on some estimates of nonincreasing rearrangements and the applications of B p weights.
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This work is in part supported by NSFC (No. 10931001, 10871173) and Natural Science Foundation of Zhejiang Province (No. Y6110415).
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Li, H., Sun, Q. Some notes on embedding for anisotropic Sobolev spaces. Czech Math J 61, 97–111 (2011). https://doi.org/10.1007/s10587-011-0020-3
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DOI: https://doi.org/10.1007/s10587-011-0020-3