This is an announcement for the paper "Conditioned square functions for non-commutative martingales" by Narcisse Randrianantoanina.

Abstract: We prove a weak-type (1,1) inequality involving conditioned square functions of martingales in non-commutative $L^p$-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the non-commutative Burkholder/Rosenthal inequalities from Ann. Proba. 31 (2003), 948-995. We also discuss BMO-norms of sums of non-commuting order independent operators.

Archive classification: Functional Analysis; Probability

Mathematics Subject Classification: 46L53; 60G42

Remarks: 38 pages

The source file(s), condsquaref.tex: 107932 bytes, is(are) stored in gzipped form as 0509226.gz with size 31kb. The corresponding postcript file has gzipped size 136kb.

Submitted from: randrin@muohio.edu

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