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NONCOMMUTATIVE MAXIMAL INEQUALITIES ASSOCIATED WITH CONVEX FUNCTIONS.
- Source :
- Transactions of the American Mathematical Society; Jan2017, Vol. 369 Issue 1, p409-427, 19p
- Publication Year :
- 2017
-
Abstract
- We prove several noncommutative maximal inequalities associated with convex functions, including a Doob type inequality for a convex function of maximal operators on noncommutative martingales, and noncommutative Dunford-Schwartz and Stein maximal ergodic inequalities for a convex function of positive and symmetric positive contractions. The key ingredient in our proofs is a Marcinkiewicz type interpolation theorem for a convex function of maximal operators in the noncommutative setting, which we establish in this paper. These generalize the results of Junge and Xu in the L<subscript>p</subscript> case to the case of convex functions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 369
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 118896729
- Full Text :
- https://doi.org/10.1090/tran/6663