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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Singular integrals on symmetric spaces, II


Author: Alexandru D. Ionescu
Journal: Trans. Amer. Math. Soc. 355 (2003), 3359-3378
MSC (2000): Primary 22E46, 43A85
Published electronically: April 25, 2003
MathSciNet review: 1974692
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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
Email: aionescu@math.mit.edu, ionescu@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03312-9
PII: S 0002-9947(03)03312-9
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
Article copyright: © Copyright 2003 American Mathematical Society