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

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.