A Characterization of BMO^\alpha-martingale spaces by fractional Carleson measures

TL;DR

This paper characterizes BMO^-martingale spaces using fractional Carleson measures, enabling easier proofs of boundedness of martingale transforms and square functions, and establishing a martingale Carleson inequality.

Contribution

It introduces a new characterization of BMO^-martingale spaces via fractional Carleson measures, facilitating analysis of martingale operators.

Findings

Boundedness of martingale transform on BMO^-martingale spaces

Boundedness of square function on BMO^-martingale spaces

Martingale version of Carleson's inequality

Abstract

We give a characterization of $BMO^\alpha$-martingale spaces by using fractional Carleson measures. We get the boudedness of martingale transform and square function on $BMO^\alpha$-martingale spaces easily by using this characterization. We also proved the martingale version of Carleson's inequality related with $BMO^\alpha$-martingales.