Weighted Sobolev spaces and embedding theorems

@article{Goldshtein2007WeightedSS,
  title={Weighted Sobolev spaces and embedding theorems},
  author={Vladimir Gol'dshtein and A. Ukhlov},
  journal={Transactions of the American Mathematical Society},
  year={2007},
  volume={361},
  pages={3829-3850}
}
In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A p -condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for smooth domains and domains with boundary singularities. The proposed method is based on the concept of 'generalized' quasiconformal homeomorphisms (homeomorphisms with bounded mean distortion). The choice of the homeomorphism type depends on the choice of… 

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