WEIGHTED MAXIMAL INEQUALITIES FOR MARTINGALES

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.