Revisiting Riesz transforms on Heisenberg groups

被引：6

作者：

Sanjay, P. K. ^{[1
,2
]}

Thangavelu, Sundaram ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Natl Inst Technol, Dept Math, Calicut 673601, Kerala, India

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2012年 / 28卷 / 04期

关键词：

Riesz transforms; Heisenberg groups; Fourier multipliers; Hermite functions; Laguerre functions; LAGUERRE FUNCTION EXPANSIONS; NILPOTENT GROUPS; SINGULAR-INTEGRALS; BOUNDED OPERATORS; HARMONIC-ANALYSIS; WEYL TRANSFORM;

D O I：

10.4171/RMI/704

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.

引用

页码：1091 / 1108

页数：18

共 23 条

[1]

[Anonymous], 1971, PRINCETON MATH SER

[2]

[Anonymous], 1993, LECT HERMITE LAGUERR

[3] WEAK (1,1) BOUNDS FOR OSCILLATORY SINGULAR-INTEGRALS [J].

CHANILLO, S ;

CHRIST, M .

DUKE MATHEMATICAL JOURNAL, 1987, 55 (01) :141-155

[4] HILBERT-TRANSFORMS ALONG CURVES .1. NILPOTENT GROUPS [J].

CHRIST, M .

ANNALS OF MATHEMATICS, 1985, 122 (03) :575-596

[5] About Riesz transforms on the Heisenberg groups [J].

Coulhon, T ;

Muller, D ;

Zienkiewicz, J .

MATHEMATISCHE ANNALEN, 1996, 305 (02) :369-379

[6] FUNDAMENTAL SOLUTION FOR A SUBELLIPTIC OPERATOR [J].

FOLLAND, GB .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (02) :373-376

[7] SPHERICAL-HARMONICS, THE WEYL TRANSFORM AND THE FOURIER-TRANSFORM ON THE HEISENBERG-GROUP [J].

GELLER, D .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1984, 36 (04) :615-684

[8]

Gutiérrez CE, 2001, HOUSTON J MATH, V27, P579

[9] Lp-dimension free boundedness for Riesz transforms associated to Hermite functions [J].

Harboure, E ;

de Rosa, L ;

Segovia, C ;

Torrea, JL .

MATHEMATISCHE ANNALEN, 2004, 328 (04) :653-682

[10] Group invariance and Lp-bounded operators [J].

Kobayashi, Toshiyuki ;

Nilsson, Andreas .

MATHEMATISCHE ZEITSCHRIFT, 2008, 260 (02) :335-354

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