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

• 成果类型: Article
• 署名作者: Li, Xiang-Dong
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Fudan University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0270-2
• 发表日期: 2011
• 页码: 111-144
• 关键词: riesz transforms; differential forms; heat kernel; curvature operator; inequalities; martingale; VARIETIES; laplacian; INTEGRALS; sharp

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.