Some remarks to a compact imbedding of a weighted Sobolev space defined on an unbounded domain. (English) Zbl 0619.46033

A. Haar Mem. Conf., Budapest/Hung. 1985, Colloq. Math. Soc. János Bolyai 49, 667-673 (1987).
[For the entire collection see Zbl 0607.00008.]
The paper deals with the compact imbedding of a weighted Sobolev space \(W_ 0^{k,p}(\Omega,S)\) (S is a collection of weight functions) defined on an unbounded domain \(\Omega\) in a weighted Lebesgue space \(L^ p(\Omega,\rho)\) (\(\rho\) is a weight function). This imbedding is investigated as the limit case of the compact imbeddings of Sobolev spaces defined on bounded domains. There are given two examples, one deals with power weights, the other with exponential weights.


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.)


Zbl 0607.00008