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Journal of Operator Theory

Volume 73, Issue 2, Spring 2015  pp. 515-532.

Weak-type interpolation for noncommutative maximal operators

Authors:  Sjoerd Dirksen
Author institution:Universitaet Bonn, Hausdorff Center for Mathematics, Endenicher Allee 60, 53115 Bonn, Germany

Summary: We prove a Boyd-type interpolation result for noncommutative maximal operators of restricted weak type. Our result positively answers an open question in T. Bekjan, Z. Chen, A. Os{\c{e}}kowski, arXiv: 1108.2795 [math.OA]. As a special case, we find a restricted weak type version of the noncommutative Marcinkiewicz interpolation theorem, due to Junge and Xu, with interpolation constant of optimal order.

Keywords: noncommutative symmetric spaces, Doob's maximal inequality, noncommutative maximal inequalities, interpolation theory

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