Inequality for Burkholder's martingale transform

Abstract

We find the sharp constant $C=C(\tau ,p,\mathbb{E}G,\mathbb{E}F)$ of the following inequality $\Vert (G^2+{\tau }^2{F}^2{)}^{1/2}{\Vert }_p\le C\Vert F{\Vert }_p,$ where $G$ is the transform of a martingale $F$ under a predictable sequence $\epsilon$ with absolute value 1, $1<p<2$, and $\tau$ is any real number.

34 pages, 13 figures

Cited by in corpus (2)

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