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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New proof of the Hörmander multiplier theorem on compact manifolds without boundary
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by Xiangjin Xu
Proc. Amer. Math. Soc. 135 (2007), 1585-1595
DOI: https://doi.org/10.1090/S0002-9939-07-08687-X
Published electronically: January 9, 2007

Abstract:

On compact manifolds $(M, g)$ without boundary, the gradient estimates for unit band spectral projection operators $\chi _{\lambda }$ are proved for a second order elliptic differential operator $L$. A new proof of the Hörmander Multiplier Theorem (first proved by A. Seeger and C.D. Sogge in 1989) is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.
References
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Bibliographic Information
  • Xiangjin Xu
  • Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720
  • Address at time of publication: Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, Virginia 22904
  • Email: xiangjxu@msri.org, xx8n@virginia.edu
  • Received by editor(s): September 15, 2005
  • Received by editor(s) in revised form: February 28, 2006
  • Published electronically: January 9, 2007
  • Communicated by: Andreas Seeger
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 1585-1595
  • MSC (2000): Primary 58J40, 35P20, 35J25
  • DOI: https://doi.org/10.1090/S0002-9939-07-08687-X
  • MathSciNet review: 2276671