On Burkholder function for orthogonal martingales and zeros of Legendre polynomials

Alexander Borichev, Prabhu Janakiraman, Alexander Volberg

Burkholder obtained a sharp estimate of $\E|W|^p$ via $\E|Z|^p$, where $W$ is a martingale transform of $Z$, or, in other words, for martingales $W$ differentially subordinated to…