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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Self-improvement of pointwise Hardy inequality


Authors: Sylvester Eriksson-Bique and Antti V. Vähäkangas
Journal: Trans. Amer. Math. Soc. 372 (2019), 2235-2250
MSC (2010): Primary 31C15; Secondary 31E05, 35A23
DOI: https://doi.org/10.1090/tran/7826
Published electronically: April 4, 2019
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Abstract: We prove the self-improvement of a pointwise $ p$-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.


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Additional Information

Sylvester Eriksson-Bique
Affiliation: Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, California 90095
Email: syerikss@math.ucla.edu

Antti V. Vähäkangas
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
Email: antti.vahakangas@iki.fi

DOI: https://doi.org/10.1090/tran/7826
Keywords: Self-improvement, pointwise Hardy inequality, uniform fatness, metric space
Received by editor(s): October 29, 2018
Received by editor(s) in revised form: February 9, 2019
Published electronically: April 4, 2019
Additional Notes: The first author was partially supported by grant #DMS-1704215 of the NSF (U.S.).
The first author also thanks Enrico Le Donne, Riikka Korte, and Juha Kinnunen for hosting and supporting visits at the University of Jyväskylä and Aalto University during which this research was completed.
Article copyright: © Copyright 2019 American Mathematical Society