The paper contains the proofs of sharp moment estimates for Hilbert-space valued martingales under the assumptions of differential subordination and orthogonality. The results generalize those obtained by Banuelos and Wang. As an application, we sharpen an inequality for stochastic integrals with respect to Brownian motion.
"Sharp and Strict $L^p$-Inequalities for Hilbert-Space-Valued Orthogonal Martingales." Electron. J. Probab. 16 531 - 551, 2011. https://doi.org/10.1214/EJP.v16-865