Singular integrals on symmetric spaces, II

Alexandru D. Ionescu

doi:10.1090/S0002-9947-03-03312-9

Singular integrals on symmetric spaces, II

Alexandru D. Ionescu

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

18 Scopus citations

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 double-struck K sign;-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 Ho'rmander-Michlin type.

Original language	English (US)
Pages (from-to)	3359-3378
Number of pages	20
Journal	Transactions of the American Mathematical Society
Volume	355
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9947-03-03312-9
State	Published - Aug 2003
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-03-03312-9

Cite this

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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 double-struck K sign;-bi-invariant kernels with certain large scale cancellation properties. As an application we prove Lp boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Ho'rmander-Michlin type.",

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AB - 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 double-struck K sign;-bi-invariant kernels with certain large scale cancellation properties. As an application we prove Lp boundedness of operators defined by Fourier multipliers that satisfy singular differential inequalities of the Ho'rmander-Michlin type.

UR - https://www.scopus.com/pages/publications/0041743839

UR - https://www.scopus.com/pages/publications/0041743839#tab=citedBy

U2 - 10.1090/S0002-9947-03-03312-9

DO - 10.1090/S0002-9947-03-03312-9

M3 - Article

AN - SCOPUS:0041743839

SN - 0002-9947

VL - 355

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EP - 3378

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -

Singular integrals on symmetric spaces, II

Abstract

All Science Journal Classification (ASJC) codes

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