Tohoku Mathematical Journal

Weighted maximal inequalities for martingales

Adam Osȩkowski

Full-text: Open access

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.

Article information

Source
Tohoku Math. J. (2), Volume 65, Number 1 (2013), 75-91.

Dates
First available in Project Euclid: 8 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1365452626

Digital Object Identifier
doi:10.2748/tmj/1365452626

Mathematical Reviews number (MathSciNet)
MR3049641

Zentralblatt MATH identifier
1266.60081

Subjects
Primary: 60G44: Martingales with continuous parameter
Secondary: 60G46: Martingales and classical analysis

Keywords
Maximal function weighted inequality martingale

Citation

Osȩkowski, Adam. Weighted maximal inequalities for martingales. Tohoku Math. J. (2) 65 (2013), no. 1, 75--91. doi:10.2748/tmj/1365452626. https://projecteuclid.org/euclid.tmj/1365452626


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