Martingale hardy spaces for 0<p≦1

Abstract

The relation between the usually considered martingale Hardy spaces is examined. It will be shown that if the stochastic basis is regular, then all these Hardy spaces are equivalent. An atomic description of the spacesH − andP p will be given for 0<p≦1 and with the help of this we shall consider the duals of these spaces. Moreover, the dual space ofVMO p generated by the dual space ofH p − will be determined in the case when all σ-algebras are generated by countably many atoms. Furthermore, we shall show in this case that the dual ofVMO 1 isH 1 − .