This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. The Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. As an application, we prove the weak type Φ-moment Burkholder-Gundy inequality for noncommutative martingales through establishing a weak type Φ-moment noncommutative Khinchin inequality for Rademacher random variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-1,
author = {Turdebek N. Bekjan and Zeqian Chen and Peide Liu and Yong Jiao},
title = {Noncommutative weak Orlicz spaces and martingale inequalities},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {195-212},
zbl = {1236.46057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-1}
}
Turdebek N. Bekjan; Zeqian Chen; Peide Liu; Yong Jiao. Noncommutative weak Orlicz spaces and martingale inequalities. Studia Mathematica, Tome 204 (2011) pp. 195-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm204-3-1/