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Maximal function estimates and self-improvement results for Poincaré inequalities

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Abstract

Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.

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Acknowledgements

Funding was provided by Academy of Finland.

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Authors and Affiliations

  1. Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Espoo, Finland

    Juha Kinnunen

  2. Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35, 40014, Jyväskylä, Finland

    Juha Lehrbäck & Antti V. Vähäkangas

  3. Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, 00014, Helsinki, Finland

    Xiao Zhong

Authors
  1. Juha Kinnunen
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  2. Juha Lehrbäck
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  3. Antti V. Vähäkangas
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  4. Xiao Zhong
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Corresponding author

Correspondence to Antti V. Vähäkangas.

Additional information

The research is supported by the Academy of Finland.

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Kinnunen, J., Lehrbäck, J., Vähäkangas, A.V. et al. Maximal function estimates and self-improvement results for Poincaré inequalities. manuscripta math. 158, 119–147 (2019). https://doi.org/10.1007/s00229-018-1016-1

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  • DOI: https://doi.org/10.1007/s00229-018-1016-1

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