Martingale transforms and Lp-supercript stop-norm estimates of Riesz transforms on complete Riemannian manifolds

• 成果类型: Article
• 署名作者: Li, Xiang-Dong
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0085-y
• 发表日期: 2008
• 页码: 247-281
• 关键词: symmetric diffusion operators; paley-stein inequality; STOCHASTIC INTEGRALS; sharp inequalities; beurling-ahlfors; heat kernel; laplacian; constants; THEOREMS; SPACES

摘要

Under the condition that the Bakry-Emery Ricci curvature is bounded from below, we prove a probabilistic representation formula of the Riesz transforms associated with a symmetric diffusion operator on a complete Riemannian manifold. Using the Burkholder sharp L-p-inequality for martingale transforms, we obtain an explicit and dimension-free upper bound of the L-p-norm of the Riesz transforms on such complete Riemannian manifolds for all 1 < p < infinity. In the Euclidean and the Gaussian cases, our upper bound is asymptotically sharp when p -> 1 and when p -> infinity.