Singular integrals on symmetric spaces of real rank one

Alexandru D. Ionescu

doi:10.1215/S0012-7094-02-11415-X

Singular integrals on symmetric spaces of real rank one

Alexandru D. Ionescu

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

In this paper we prove a new variant of the Herz majorizing principle for operators defined by K-bi-invariant kernels with certain large-scale cancellation properties. As an application, we prove L^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^p-norm of large imaginary powers of the critical L^p-Laplacian.

Original language	English (US)
Pages (from-to)	101-122
Number of pages	22
Journal	Duke Mathematical Journal
Volume	114
Issue number	1
DOIs	https://doi.org/10.1215/S0012-7094-02-11415-X
State	Published - Jul 15 2002

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/S0012-7094-02-11415-X

Cite this

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

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Singular integrals on symmetric spaces of real rank one

Abstract

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