Noncommutative integral inequalities for convex functions of maximal functions and applications

Details Noncommutative integral inequalities for convex functions of maximal functions and applications Noncommutative integral inequalities for convex functions of maximal functions and applications

2011-08-13

arxiv.org/abs/1108.2795v4

Mathematics

Operator Algebras

16 pages

Scientific paper

In this paper, we establish a Marcinkiewicz type interpolation theorem for convex functions of maximal functions in the noncommutative setting. As applications, we prove the noncommutative analogue of the Doob inequality for convex functions of maximal functions on martingales, the analogue of the classical Dunford-Schwartz maximal ergodic inequality for convex functions of positive contractions, and that of Stein's maximal inequality for convex functions of symmetric positive contractions. As a consequence, we obtain the moment Burkholder-Davis-Gundy inequality for noncommutative martingales.

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