Martingale transforms and \(L^p\)-norm estimates of Riesz transforms on complete Riemannian manifolds

DOI10.1007/s00440-007-0085-yzbMath1140.53022OpenAlexW1987850253MaRDI QIDQ2480828

Xiang Dong Li

Publication date: 3 April 2008

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-007-0085-y

zbMATH Keywords

Riesz transformsBakry-Emery Ricci curvaturemartingale transformsBurkholder sharp \(L^p\)-inequality for martingale subordination

Mathematics Subject Classification ID

Brownian motion (60J65) Pseudodifferential and Fourier integral operators on manifolds (58J40) Diffusion processes and stochastic analysis on manifolds (58J65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (16)

Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups ⋮ The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ The second-order gradient estimates for the V-heat kernel and its applications ⋮ Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundles ⋮ Martingale transforms and their projection operators on manifolds ⋮ Bellman function and linear dimension-free estimates in a theorem of Bakry ⋮ Bilinear embedding for real elliptic differential operators in divergence form with potentials ⋮ Dimension free \(L^p\) estimates for single Riesz transforms via an \(H^\infty\) joint functional calculus ⋮ Variable exponent spaces of differential forms on Riemannian manifold ⋮ \(L^p\)-estimates and existence theorems for the \(\bar \partial\)-operator on complete Kähler manifolds ⋮ Riesz transforms on forms and \(L^p\)-Hodge decomposition on complete Riemannian manifolds ⋮ On the weak \(L ^{p }\)-Hodge decomposition and Beurling--Ahlfors transforms on complete Riemannian manifolds ⋮ Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space ⋮ On the strong \(L^p\)-Hodge decomposition over complete Riemannian manifolds ⋮ Noncommutative martingale deviation and Poincaré type inequalities with applications ⋮ Sobolev–Kantorovich inequalities under CD(0,∞) condition

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