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Generalized doubling meets Poincaré

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Abstract

We establish a modified segment inequality on metric spaces that satisfy a generalized volume doubling property. This leads to Sobolev and Poincaré inequalities for such spaces. We also give several examples of spaces that satisfy the generalized doubling condition.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, 90095, Los Angeles, CA

    Colin Hinde & Peter Petersen

Authors
  1. Colin Hinde
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  2. Peter Petersen
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Correspondence to Colin Hinde.

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Communicated by Robert E. Greene

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Hinde, C., Petersen, P. Generalized doubling meets Poincaré. J Geom Anal 17, 485–494 (2007). https://doi.org/10.1007/BF02922093

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  • DOI: https://doi.org/10.1007/BF02922093

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