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Singular integrals on symmetric spaces, II

Author(s): Alexandru D. Ionescu
Journal: Trans. Amer. Math. Soc. 355 (2003), 3359-3378.
MSC (2000): Primary 22E46, 43A85
Posted: April 25, 2003
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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: 10.1090/S0002-9947-03-03312-9
PII: S 0002-9947(03)03312-9
Received by editor(s): September 12, 2001
Posted: April 25, 2003
Additional Notes: The author was supported in part by the National Science Foundation under NSF Grant No. 0100021
Copyright of article: Copyright 2003, American Mathematical Society

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