Resumen de The martingale Smirnov class

M. Nawrocki

• The Smirnov class $N_\ast(\delta)$ of dyadic martingales is studied. Continuous linear functionals on this class and its Fréchet envelope are described. It is proved that, in contrast to the case of $H^p$-spaces, the space $N_\ast(\delta)$ is not isomorphic to the Smirnov class of holomorphic functions on the unit disc. Finally, atomic decompositions of elements of $N_\ast(\delta)$ are obtained.