Spectral Multipliers for the Kohn Laplacian on Forms on the Sphere in Cn

被引：0

作者：

Casarino, Valentina ^{[1
]}

Cowling, Michael G. ^{[2
]}

Martini, Alessio ^{[3
]}

Sikora, Adam ^{[4
]}

机构：

[1] Univ Padua, Dipartimento Tecn & Gest Sistemi Ind, Stradella San Nicola 3, I-36100 Vicenza, Italy

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[3] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands, England

[4] Macquarie Univ, Dept Math, Sydney, NSW 2109, Australia

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2017年 / 27卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Cauchy-Riemann complex; Kohn Laplacian; Multiplier theorem; HYPOELLIPTIC DIFFERENTIAL-OPERATORS; RIESZ MEANS; EIGENFUNCTION-EXPANSIONS; HEISENBERG-GROUP; NILPOTENT GROUPS; WAVE-EQUATION; SUBLAPLACIAN; COMPLEX; BOUNDS;

D O I：

10.1007/s12220-017-9806-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The unit sphere S in C-n is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian square(b). We prove a Hormander spectral multiplier theorem square(b) for with critical index n-1/2, that is, half the topological dimension of S. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on S.

引用

页码：3302 / 3338

页数：37

共 37 条

[1] [Anonymous], 2015, Mem. Amer. Math. Soc.
[2] [Anonymous], 1996, Progress in Mathematics
[3] The subelliptic heat kernel on the CR sphere
Baudoin, Fabrice
Wang, Jing
[J]. MATHEMATISCHE ZEITSCHRIFT, 2013, 275 (1-2) : 135 - 150
[4] Boggess A., 1991, CR manifolds and the Tangential Cauchy-Riemann Complex
[5] Lp-summability of Riesz means for the sublaplacian on complex spheres
Casarino, Valentina
Peloso, Marco M.
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2011, 83 : 137 - 152
[6] Hopf fibration: Geodesics and distances
Chang, Der-Chen
Markina, Irina
Vasil'ev, Alexander
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2011, 61 (06) : 986 - 1000
[7] LP BOUNDS FOR SPECTRAL MULTIPLIERS ON NILPOTENT GROUPS
CHRIST, M
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 328 (01) : 73 - 81
[8] A spectral multiplier theorem for a sublaplacian on SU(2)
Cowling, M
Sikora, A
[J]. MATHEMATISCHE ZEITSCHRIFT, 2001, 238 (01) : 1 - 36
[9] Cowling M.G., 2013, Trends in Harmonic Analysis, P147
[10] SPECTRAL MULTIPLIERS FOR THE KOHN SUBLAPLACIAN ON THE SPHERE IN C
Cowling, Michael G.
Klima, Oldrich
Sikora, Adam
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (02) : 611 - 631

← 1 2 3 4 →