Tohoku Mathematical Journal
2013

March
SECOND SERIES VOL. 65, NO. 1

Tohoku Math. J.
65 (2013), 75-91

Title WEIGHTED MAXIMAL INEQUALITIES FOR MARTINGALES

Author Adam Osȩkowski

(Received March 14, 2012, revised July 9, 2012)
Abstract. 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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