Perturbation of Burkholder's martingale transform and Monge--Ampère equation

Nicholas Boros, Prabhu Janakiraman, Alexander Volberg

Let $\{d_k{\}}_{k\ge 0}$ be a complex martingale difference in $L^p[0,1],$ where $1<p<\infty ,$ and $\{\e_k\}_{k \geq 0}$ a sequence in $\{\pm 1\}.$ We obtain the following generali…