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Weighted Inequalities of Poincaré Type on Chain Domains

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Harmonic Analysis, Partial Differential Equations and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

We provide an abstract version of a chain argument used in deriving Poincaré type inequalities on Boman domains. No doubling conditions need to be assumed for this abstract version. It unifies various results on chain domains that include ϕ-John domains. Besides Poincaré type inequalities, it works also for fractional Poincaré inequalities on quasimetric spaces.

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Acknowledgements

The author would like to thank the referee for his suggestion in improving the paper. The author would also like to take this opportunity to thank Professor Wheeden for his guidance and patience while he was a graduate student at Rutgers University 30 years ago.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10, Lower Kent Ridge Road, Singapore, 119076, Singapore

    Seng-Kee Chua

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  1. Seng-Kee Chua
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Correspondence to Seng-Kee Chua .

Editor information

Editors and Affiliations

  1. Dept. of Math, Rutgers University, Piscataway, New Jersey, USA

    Sagun Chanillo

  2. Department of Mathematics, University of Bologna, Bologna, Italy

    Bruno Franchi

  3. Dept. of Math., Univ. of Connecticut, Storrs CT, USA

    Guozhen Lu

  4. Department of Mathematics, University of Bilbao, Bilbao, Spain

    Carlos Perez

  5. Dept of Math and Stat, McMaster University, Hamilton, Ontario, Canada

    Eric T. Sawyer

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Chua, SK. (2017). Weighted Inequalities of Poincaré Type on Chain Domains. In: Chanillo, S., Franchi, B., Lu, G., Perez, C., Sawyer, E. (eds) Harmonic Analysis, Partial Differential Equations and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52742-0_3

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