### A Hardy space related to the square root of the Poisson kernel

A real-valued Hardy space $H{\xb9}_{\surd}\left(\right)\subseteq L\xb9\left(\right)$ related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in $H{\xb9}_{\surd}\left(\right)$ if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to $H{\xb9}_{\surd}\left(\right)$, and no Orlicz space...