Discrete Hardy Spaces Related to Powers of the Poisson Kernel - Vasilis, Jonatan (Mathematica Scandinavica, 2013)
Discrete Hardy spaces H^1_α(T), related to powers α 1/2 of the Poisson kernels on boundaries T of regular rooted trees, are studied. The spaces for α > 1/2 coincide with the ordinary atomic Hardy space on T, which in turn is strictly smaller than H^1_1/2(T). The Orlicz space LL(T) characterizes the positive and increasing functions in H^1_1/2(T), but there is no such characterization for general positive functions.