## Osaka Journal of Mathematics

### Sharp maximal estimates for BMO martingales

#### Abstract

We introduce a method which can be used to study maximal inequalities for martingales of bounded mean oscillation. As an application, we establish sharp $\Phi$-inequalities and tail inequalities for the one-sided maximal function of a BMO martingale. The results can be regarded as BMO counterparts of the classical maximal estimates of Doob.

#### Article information

Source
Osaka J. Math., Volume 52, Number 4 (2015), 1125-1143.

Dates
First available in Project Euclid: 18 November 2015

https://projecteuclid.org/euclid.ojm/1447856036

Mathematical Reviews number (MathSciNet)
MR3426632

Zentralblatt MATH identifier
1331.60074

Subjects
Primary: 60G42: Martingales with discrete parameter
Secondary: 60G44: Martingales with continuous parameter

#### Citation

Osȩkowski, Adam. Sharp maximal estimates for BMO martingales. Osaka J. Math. 52 (2015), no. 4, 1125--1143. https://projecteuclid.org/euclid.ojm/1447856036

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