Theory of Hp-spaces for continuous filtrations in Von Neumann algebras
By: Marius Junge, Mathilde Perrin
Contributors: Perrin, Mathilde, author; Société mathématique de France
Series: Astérisque -- 362
Publisher: Société mathématique de France
Published: 2014
Place of publication: Paris
Language: eng
Number of pages: 134
ISBN-13: 9782856297896
Subjects: Noncommutative algebras; Hardy spaces; Von Neumann algebras
Description: We introduce Hardy spaces for martingales with respect to continuous filtration for von Neumann algebras. In particular we prove the analogues of the Burkholder-Gundy and Burkholder-Rosenthal inequalities in this setting. The usual arguments using stopping times in the commutative case are replaced by tools from noncommutative function theory and allow us to obtain the analogue of the Feffermann-Stein duality and prove a noncommutative Davis decomposition.--Provided by publisher
Notes: Includes bibliographical references (pages 131-134).