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.
Citation
Adam Osȩkowski. "Weighted maximal inequalities for martingales." Tohoku Math. J. (2) 65 (1) 75 - 91, 2013. https://doi.org/10.2748/tmj/1365452626
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