TY - JOUR
AU - Jonatan Vasilis
PY - 2013/06/01
Y2 - 2020/11/26
TI - Discrete Hardy Spaces Related to Powers of the Poisson Kernel
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 112
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-15243
UR - https://www.mscand.dk/article/view/15243
AB - Discrete Hardy spaces $H^{1}_{\alpha}(\partial{T})$, related to powers $\alpha \ge 1/2$ of the Poisson kernels on boundaries $\partial{T}$ of regular rooted trees, are studied. The spaces for $\alpha > 1/2$ 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.
ER -