## Some notes on embedding for anisotropic Sobolev spaces.(English)Zbl 1224.46065

Summary: 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.

### MSC:

 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 42B35 Function spaces arising in harmonic analysis
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### References:

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