Singular integrals on symmetric spaces of real rank one

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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 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.

Original languageEnglish (US)
Pages (from-to)101-122
Number of pages22
JournalDuke Mathematical Journal
Volume114
Issue number1
DOIs
StatePublished - Jul 15 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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