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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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