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Ends of metric measure spaces and Sobolev inequalities

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Abstract

Generalizing work of Li and Wang, we prove sharp volume growth/decay rates for ends of metric measure spaces supporting a (p,p)-Sobolev inequality. A sharp result for (q,p)-Sobolev inequalities is also proved.

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Authors and Affiliations

  1. Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland

    Stephen M Buckley

  2. Department of Mathematics, University of Jyväskylä, P.O. Box 35, Fin-40014, Jyväskylä, Finland

    Pekka Koskela

Authors
  1. Stephen M Buckley
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  2. Pekka Koskela
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Correspondence to Stephen M Buckley.

Additional information

The first author was partially supported by Enterprise Ireland.

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Buckley, S., Koskela, P. Ends of metric measure spaces and Sobolev inequalities. Math. Z. 252, 275–285 (2006). https://doi.org/10.1007/s00209-005-0846-1

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  • DOI: https://doi.org/10.1007/s00209-005-0846-1

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