manuscripta mathematica

, Volume 158, Issue 1–2, pp 119–147 | Cite as

Maximal function estimates and self-improvement results for Poincaré inequalities

  • Juha Kinnunen
  • Juha Lehrbäck
  • Antti V. VähäkangasEmail author
  • Xiao Zhong


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.

Mathematics Subject Classification

42B25 35A23 46E35 31E05 30L99 


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Funding was provided by Academy of Finland.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsAalto UniversityEspooFinland
  2. 2.Department of Mathematics and StatisticsUniversity of JyvaskylaJyväskyläFinland
  3. 3.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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