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Continuous and compact imbeddings of weighted Sobolev spaces. I. (English) Zbl 0676.46030
Summary: We establish some conditions on p, q and the weight functions \(v_ 0\), \(v_ 1\), w under which the continuous imbedding \[ (1.1)\quad W^{1,p}(\Omega;v_ 0,v_ 1)\hookrightarrow L^ q(\Omega;w), \] or the compact imbedding \[ (1.2)\quad W^{1,p}(\Omega;v_ 0,v_ 1)\hookrightarrow \hookrightarrow L^ q(\Omega;w) \] takes place.

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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References:
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