Hardy spaces of differential forms on Riemannian manifolds

被引：160

作者：

Auscher, Pascal ^{[1
,2
]}

McIntosh, Alan ^{[3
]}

Russ, Emmanuel ^{[4
]}

机构：

[1] Univ Paris Sud, Orsay, France

[2] Univ Paris Sud, CNRS, UMR 8628, F-91405 Orsay, France

[3] Australian Natl Univ, Inst Math Sci, Ctr Math & Applicat, Canberra, ACT 0200, Australia

[4] Univ Paul Cezanne, Fac Sci & Tech, CNRS UMR 6632, LATP, F-13397 Marseille 20, France

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2008年 / 18卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

Riemannian manifolds; Hardy spaces; differential forms; Riesz transforms;

D O I：

10.1007/s12220-007-9003-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H-p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H-p-boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H-infinity functional calculus and Hodge decomposition, are given.

引用

页码：192 / 248

页数：57

共 51 条

[1] Riesz transform on manifolds and heat kernel regularity [J].

Auscher, P ;

Coulhon, T ;

Duong, XT ;

Hofmann, S .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2004, 37 (06) :911-957

[2] Hardy spaces and divergence operators on strongly Lipschitz domains of Rn [J].

Auscher, P ;

Russ, E .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 201 (01) :148-184

[3] The solution of the Kato square root problem for second order elliptic operators on Rn [J].

Auscher, P ;

Hofmann, S ;

Lacey, M ;

McIntosh, A ;

Tchamitchian, P .

ANNALS OF MATHEMATICS, 2002, 156 (02) :633-654

[4] FUNCTIONAL-CALCULUS FOR A CLASS OF COMPLEX ELLIPTIC-OPERATORS IN DIMENSION ONE (AND APPLICATIONS TO SOME COMPLEX ELLIPTIC-EQUATIONS IN DIMENSION-2) [J].

AUSCHER, P ;

TCHAMITCHIAN, P .

ANNALES DE L INSTITUT FOURIER, 1995, 45 (03) :721-+

[5]

AUSCHER P, 1998, ASTERIQUE, V249

[6]

AUSCHER P, UNPUB BOUNDEDNESS BA

[7]

Auscher P, 2007, MEM AM MATH SOC, V186, pXI

[8] Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds [J].

Auscher, Pascal ;

McIntosh, Alan ;

Russ, Emmanuel .

COMPTES RENDUS MATHEMATIQUE, 2007, 344 (02) :103-108

[9] Quadratic estimates and functional calculi of perturbed Dirac operators [J].

Axelsson, A ;

Keith, S ;

McIntosh, A .

INVENTIONES MATHEMATICAE, 2006, 163 (03) :455-497

[10]

BAKRY D, 1987, LECT NOTES MATH, V1247, P137

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