On the weak L (p) -Hodge decomposition and Beurling-Ahlfors transforms on complete Riemannian manifolds

doi:10.1007/s00440-010-0270-2

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	On the weak L (p) -Hodge decomposition and Beurling-Ahlfors transforms on complete Riemannian manifolds
	Li, Xiang-Dong1,2,3
	2011-06-01
发表期刊	PROBABILITY THEORY AND RELATED FIELDS
ISSN	0178-8051
卷号	150 期号:1-2 页码:111-144
摘要	Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the L (p) -norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak L (p) -Hodge decomposition theorem and to prove the L (p) -boundedness of the Beurling-Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenbock curvature operator.
关键词	Beurling-Ahlfors transforms Hodge decomposition Martingale representation formula Weitzenbck curvature
DOI	10.1007/s00440-010-0270-2
语种	英语
资助项目	Chinese Academy of Sciences, NSFC[10971032] ; Shanghai Pujiang Talent Project[09PJ1401600] ; Key Laboratory RCSDS, CAS[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000290725200005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12143
专题	应用数学研究所
通讯作者	Li, Xiang-Dong
作者单位	1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 3.Univ Toulouse 3, Inst Math, F-31062 Toulouse 9, France
推荐引用方式 GB/T 7714	Li, Xiang-Dong. On the weak L (p) -Hodge decomposition and Beurling-Ahlfors transforms on complete Riemannian manifolds[J]. PROBABILITY THEORY AND RELATED FIELDS,2011,150(1-2):111-144.
APA	Li, Xiang-Dong.(2011).On the weak L (p) -Hodge decomposition and Beurling-Ahlfors transforms on complete Riemannian manifolds.PROBABILITY THEORY AND RELATED FIELDS,150(1-2),111-144.
MLA	Li, Xiang-Dong."On the weak L (p) -Hodge decomposition and Beurling-Ahlfors transforms on complete Riemannian manifolds".PROBABILITY THEORY AND RELATED FIELDS 150.1-2(2011):111-144.