Sobolev Spaces on an Arbitrary Metric Space

  title={Sobolev Spaces on an Arbitrary Metric Space},
  author={PIOTR HAJLASZ},
  • Published 1994
We define Sobolev space J V ' , ~ for 1 < p < (x, on an arbitrary metric space with finite diameter and equipped with finite, positive Bore1 measure. In the Euclidean case it coincides with standard Sobolev space. Several classical imbedding theorems are special cases of general results which hold in the metric case. We apply our results to weighted Sobolev space with Muckenhoupt weight. Mathematics Subject Classifications (1991). Primary: 46E35; Secondary: 28A80 
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