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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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A priori estimates for higher order multipliers on a circle
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by A. Alexandrou Himonas and Gerard Misiołek PDF
Proc. Amer. Math. Soc. 130 (2002), 3043-3050 Request permission

Abstract:

We present an elementary proof of an a priori estimate of Bourgain for a general class of multipliers on a circle using an extension of methods developed in our previous work. The main tool is a suitable version of a counting argument of Zygmund for unbounded regions.
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Additional Information
  • A. Alexandrou Himonas
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 86060
  • Email: alex.a.himonas.1@nd.edu
  • Gerard Misiołek
  • Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 – and – Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, CB3 9EW, United Kingdom
  • Email: misiolek.1@nd.edu
  • Received by editor(s): May 29, 2001
  • Published electronically: March 14, 2002
  • Additional Notes: Both authors were partially supported by the NSF under grant number DMS-9970857 and by the Faculty Research Program of the University of Notre Dame.
    The second author was also supported by the Isaac Newton Institute for Mathematical Sciences of the University of Cambridge.
  • Communicated by: Mei-Chi Shaw
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 3043-3050
  • MSC (1991): Primary 42B15; Secondary 35G25
  • DOI: https://doi.org/10.1090/S0002-9939-02-06439-0
  • MathSciNet review: 1908929