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Discrete Hardy Spaces Related to Powers of the Poisson Kernel

Jonatan Vasilis

Abstract


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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15243

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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