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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Admissible measures in one dimension


Authors: Jana Björn, Stephen Buckley and Stephen Keith
Journal: Proc. Amer. Math. Soc. 134 (2006), 703-705
MSC (2000): Primary 26D10; Secondary 46E35
Published electronically: September 28, 2005
MathSciNet review: 2180887
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Abstract: In this note we show that $ p\mspace{1mu}$-admissible measures in one dimension (i.e. doubling measures admitting a $ p\mspace{1mu}$-Poincaré inequality) are precisely the Muckenhoupt $ A_p$-weights.


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Additional Information

Jana Björn
Affiliation: Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Email: jabjo@mai.liu.se

Stephen Buckley
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, County Kildare, Ireland
Email: sbuckley@maths.may.ie

Stephen Keith
Affiliation: Centre for Mathematics and its Application, Australian National University, Canberra, ACT 0200, Australia
Email: keith@maths.anu.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07925-6
PII: S 0002-9939(05)07925-6
Keywords: Admissible measure, Muckenhoupt $A_p$-weight, doubling measure, Poincar\'e inequality
Received by editor(s): July 6, 2004
Published electronically: September 28, 2005
Additional Notes: The first author was supported by the Swedish Research Council and Gustaf Sigurd Magnuson’s fund of the Royal Swedish Academy of Sciences, and completed this research while at Lund University.
The second author was partially supported by Enterprise Ireland.
The third author was supported by the Australian Research Council.
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.