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\(A_ r\)-condition for two weight functions and compact imbeddings of weighted Sobolev spaces. (English) Zbl 0676.46029
Summary: We establish some sufficient conditions on p, q and the weight functions \(v_ 0\), \(v_ 1\), w under which the compact imbedding \[ (1.1)\quad W^{1,p}(\Omega;v_ 0,v_ 1)\hookrightarrow \hookrightarrow L^ q(\Omega;w) \] 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.)
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References:
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