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Riesz transforms on forms and L-P-Hodge decomposition on complete Riemannian manifolds
Li, Xiang-Dong1,2,3
2010
发表期刊REVISTA MATEMATICA IBEROAMERICANA
ISSN0213-2230
卷号26期号:2页码:481-528
摘要In this paper we prove the Strong LP-stability of the heat semi-group generated by the Hodge Laplacian on complete Riemannian manifolds with non-negative Weitzenbock curvature. Based on a probabilistic representation formula, we obtain an explicit upper bound of the L-p-norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak L-p-Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenbock curvature.
关键词Hodge decomposition martingale transforms Riesz transforms Weitzenbock curvature
语种英语
资助项目CNRS at the Universite Paris-Sud ; CAS[2008DP173182] ; NSFC[10971032] ; Shanghai Pujiang Talent[09PJ1401600]
WOS研究方向Mathematics
WOS类目Mathematics
WOS记录号WOS:000280972000003
出版者EUROPEAN MATHEMATICAL SOC
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/10763
专题应用数学研究所
通讯作者Li, Xiang-Dong
作者单位1.Chinese Acad Sci, AMSS, Inst Appl Math, 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
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GB/T 7714
Li, Xiang-Dong. Riesz transforms on forms and L-P-Hodge decomposition on complete Riemannian manifolds[J]. REVISTA MATEMATICA IBEROAMERICANA,2010,26(2):481-528.
APA Li, Xiang-Dong.(2010).Riesz transforms on forms and L-P-Hodge decomposition on complete Riemannian manifolds.REVISTA MATEMATICA IBEROAMERICANA,26(2),481-528.
MLA Li, Xiang-Dong."Riesz transforms on forms and L-P-Hodge decomposition on complete Riemannian manifolds".REVISTA MATEMATICA IBEROAMERICANA 26.2(2010):481-528.
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