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

Abstract

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

7 pages