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On anisotropic imbeddings. (English) Zbl 0564.46029

The paper deals with anisotropic Sobolev spaces in the sense \(W^ 1_{\bar p}=\{f;D_ if\in L_{p_ i},f\in L_{p_ 0}\}\). There is proved an imbedding of \(W^ 1_{\bar p}\) into a scale of mixed norm \(L_ p\)-spaces for \(\sum P_ i^{-1}>1\) and, further, a limit exponent theorem of the Trudinger type for \(\sum p_ i^{-1}=1\), the target space bieng an anisotropic Besov space.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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