Bellman function and linear dimension-free estimates in a theorem of Bakry

Abstract

Abstract. By using an explicit Bellman function, we prove a bilinear embedding theorem for the Laplacian associated with a weighted Riemannian manifold (M, µϕ) having the Bakry-Emery curvature bounded from below. The embedding, acting on the Cartesian product of L p (M, µϕ) and L q (T * M, µϕ),

Bellman functions and dimension free Lp-estimates for the Riesz transforms in Bessel settings

“…A fundamental ingredient for the proof of our main result is the Bellman function. A function introduced by Nazarov and Treil ( [30]) and some modifications of it have been used in different settings ( [7], [11], [12], [14], [43], and [44]). Assume that p ≥ 2.…”

Bounded holomorphic functional calculus for nonsymmetric Ornstein-Uhlenbeck operators

“…If interested in the genesis of Bellman functions and the overview of the method, the reader is also referred to [68,81,82]. The method has seen a whole series of applications, yet until recently (see [10,11]) mostly in Euclidean harmonic analysis.…”

Gundy–Varopoulos martingale transforms and their projection operators on manifolds and vector bundles

“…See also [37] for Riesz transforms of k-forms on the Heisenberg group. Last but not the least, we refer to [14] for Bellman function techniques to study Riesz transforms on manifolds under Bakry-Émery type curvature assumptions.…”