Dual spaces of dyadic Hardy spaces generated by a rearrangement invariant space X on [0,1]

Abstract

First we define the dyadic Hardy space H_X(d) for an arbitrary rearrangement invariant space X on [0, 1]. We remark that previously only a definition of H_X(d) for X with the upper Boyd index q_x<∞ was available. Then we get a natural description of the dual space of H_x, in the case X having the property 1<-p_X<-q_X<2, imporoving an earlier result [P1].