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Tohoku Mathematical Journal
SECOND SERIES VOL. 65, NO. 1
|Tohoku Math. J.|
65 (2013), 75-91
WEIGHTED MAXIMAL INEQUALITIES FOR MARTINGALES
(Received March 14, 2012, revised July 9, 2012)
The paper contains the study of sharp weighted versions of the classical Doob's weak-type estimates for real-valued martingales. As a by-product, some results concerning the structure of Muckenhoupt's classes are obtained. The proof rests on Bellman function method, i.e., it is based on the construction of a special function having appropriate concavity and majorization properties.
2000 Mathematics Subject Classification.
Primary 60G44; Secondary 60G46.
Key words and phrases.
Maximal function, weighted inequality, martingale.
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