Discrete Hardy Spaces Related to Powers of the Poisson Kernel - Vasilis, Jonatan (MATHEMATICA SCANDINAVICA, 2013)
Discrete Hardy spaces $H^{1}_{α}(\partial{T})$, related to powers $α \ge 1/2$ of the Poisson kernels on boundaries $\partial{T}$ of regular rooted trees, are studied. The spaces for $α > 1/2$ coincide with the ordinary atomic Hardy space on $\partial{T}$, which in turn is strictly smaller than $H^{1}_{1/2}(\partial{T})$. The Orlicz space $L\log\log L(\partial{T})$ characterizes the positive and increasing functions in $H^{1}_{1/2}(\partial{T})$, but there is no such characterization for general positive functions.