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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Admissible measures in one dimension
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by Jana Björn, Stephen Buckley and Stephen Keith PDF
Proc. Amer. Math. Soc. 134 (2006), 703-705 Request permission

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
  • 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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 703-705
  • MSC (2000): Primary 26D10; Secondary 46E35
  • DOI: https://doi.org/10.1090/S0002-9939-05-07925-6
  • MathSciNet review: 2180887