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Compact imbedding of weighted Sobolev space defined on an unbounded domain. II. (English) Zbl 0664.46031
The paper deals with the compact imbedding of the weighted Sobolev space \(W_ 0^{k,p}(\Omega,S)\) (S is a collection of weight functions) into the weighted Lebesgue space \(L^ p(\Omega,\rho)\) (\(\rho\) is a weight function). The domain \(\Omega\) is supposed to be unbounded and the above mentioned imbedding is investigated as a limit case of the compact imbeddings of Sobolev spaces defined on bounded domains. Examples are given dealing with power and exponential weights. For part I see ibid. 113, No.1, 60-73 (1988; Zbl 0646.46029).
Reviewer: B.Opic
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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