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15 July 2002 Singular integrals on symmetric spaces of real rank one
Alexandru D. Ionescu
Duke Math. J. 114(1): 101-122 (15 July 2002). DOI: 10.1215/S0012-7094-02-11415-X

Abstract

In this paper we prove a new variant of the Herz majorizing principle for operators defined by $\mathbb {K}$-bi-invariant kernels with certain large-scale cancellation properties. As an application, we prove $L\sp p$-boundedness of operators defined by Fourier multipliers which satisfy singular differential inequalities of the Hörmander-Michlin type. We also find sharp bounds on the $L\sp p$-norm of large imaginary powers of the critical $L\sp p$-Laplacian.

Citation

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Alexandru D. Ionescu. "Singular integrals on symmetric spaces of real rank one." Duke Math. J. 114 (1) 101 - 122, 15 July 2002. https://doi.org/10.1215/S0012-7094-02-11415-X

Information

Published: 15 July 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1007.43010
MathSciNet: MR1915037
Digital Object Identifier: 10.1215/S0012-7094-02-11415-X

Subjects:
Primary: 43A85
Secondary: ‎43A32

Rights: Copyright © 2002 Duke University Press

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Vol.114 • No. 1 • 15 July 2002
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