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Non-commutative martingale inequalities

Gilles Pisier·Quanhua Xu
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Abstract

We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be an $L^p$-martingale via its integrand, and then extend the Ito-Clifford integral theory in $L^2$, developed by Barnett, Streater and Wilde, to $L^p$ for all $1<p<\infty$. We include an appendix on the non-commutative analogue of the classical Fefferman duality between $H^1$ and $BMO$.

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Gilles Pisier, Quanhua Xu. 1997-04-04. Non-commutative martingale inequalities. https://doi.org/10.1007/s002200050224

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