Non-commutative martingale inequalities

Gilles Pisier; Quanhua Xu

doi:10.1007/s002200050224

Non-commutative martingale inequalities

Gilles Pisier^*
, Quanhua Xu

^*Corresponding author for this work

Sorbonne Université
UMR de Mathématiques

Research output: Contribution to journal › Article › peer-review

200 Scopus citations

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 L², developed by Barnett, Streater and Wilde, to L^p for all 1 < p < ∞. We include an appendix on the non-commutative analogue of the classical Fefferman duality between H¹ and BMO.

Original language	English
Pages (from-to)	667-698
Number of pages	32
Journal	Communications in Mathematical Physics
Volume	189
Issue number	3
DOIs	https://doi.org/10.1007/s002200050224
State	Published - 1997
Externally published	Yes

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title = "Non-commutative martingale inequalities",

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 Lp-martingale via its integrand, and then extend the Ito-Clifford integral theory in L2, developed by Barnett, Streater and Wilde, to Lp for all 1 < p < ∞. We include an appendix on the non-commutative analogue of the classical Fefferman duality between H1 and BMO.",

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year = "1997",

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AB - 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 Lp-martingale via its integrand, and then extend the Ito-Clifford integral theory in L2, developed by Barnett, Streater and Wilde, to Lp for all 1 < p < ∞. We include an appendix on the non-commutative analogue of the classical Fefferman duality between H1 and BMO.

UR - https://www.scopus.com/pages/publications/0031549892

U2 - 10.1007/s002200050224

DO - 10.1007/s002200050224

M3 - 文章

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SN - 0010-3616

VL - 189

SP - 667

EP - 698

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Non-commutative martingale inequalities

Abstract

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