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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Singular integrals on symmetric spaces, II
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by Alexandru D. Ionescu PDF
Trans. Amer. Math. Soc. 355 (2003), 3359-3378 Request permission

Abstract:

We extend some of our earlier results on boundedness of singular integrals on symmetric spaces of real rank one to arbitrary noncompact symmetric spaces. Our main theorem is a transference principle for operators defined by $\mathbb {K}$-bi-invariant kernels with certain large scale cancellation properties. As an application we prove $L^p$ boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Hörmander–Michlin type.
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Additional Information
  • Alexandru D. Ionescu
  • Affiliation: Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Address at time of publication: University of Wisconsin – Madison, Madison, Wisconsin 53706
  • MR Author ID: 660963
  • Email: aionescu@math.mit.edu, ionescu@math.wisc.edu
  • Received by editor(s): September 12, 2001
  • Published electronically: April 25, 2003
  • Additional Notes: The author was supported in part by the National Science Foundation under NSF Grant No. 0100021
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3359-3378
  • MSC (2000): Primary 22E46, 43A85
  • DOI: https://doi.org/10.1090/S0002-9947-03-03312-9
  • MathSciNet review: 1974692