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Mathematische Annalen

, Volume 357, Issue 3, pp 1199–1204 | Cite as

A note on “Quasihyperbolic boundary conditions and Poincaré domains”

  • Renjin Jiang
  • Aapo Kauranen
Article

Abstract

We establish optimal Poincaré inequalities under a logarithmic growth condition on the quasihyperbolic metric.

Mathematics Subject Classification (2010)

46E35 30F45 

Notes

Acknowledgments

The authors wish to thank their advisor Professor Pekka Koskela for helpful discussions.

References

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    Koskela, P., Onninen, J., Tyson, J.T.: Quasihyperbolic boundary conditions and Poincaré domains. Math. Ann. 323, 811–830 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
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    Smith, W., Stegenga, D.A.: Hölder domains and Poincaré domains. Trans. Am. Math. Soc. 319, 67–100 (1990)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Beijing Normal UniversityLaboratory of Mathematics and Complex Systems, Ministry of EducationBeijingPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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