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A Universality Property of Sobolev Spaces in Metric Measure Spaces

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Book cover Sobolev Spaces In Mathematics I

Part of the book series: International Mathematical Series ((IMAT,volume 8))

Abstract

Current research on analysis in metric measure spaces has used alternative notions of Sobolev functions on metric measure spaces. We show that, under some mild geometric assumptions on the metric measure space, all these notions give the same class of functions.

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Author information

Authors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, 45221-0025, USA

    Nageswari Shanmugalingam

Authors
  1. Nageswari Shanmugalingam
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz’ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz’ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz’ya

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Shanmugalingam, N. (2009). A Universality Property of Sobolev Spaces in Metric Measure Spaces. In: Maz’ya, V. (eds) Sobolev Spaces In Mathematics I. International Mathematical Series, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85648-3_12

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