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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:
 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 4.6e+31 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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