# The range of Hardy number on comb domains

@inproceedings{Karafyllia2021TheRO, title={The range of Hardy number on comb domains}, author={Christina Karafyllia}, year={2021} }

Let D 6= C be a simply connected domain and f be the Riemann mapping from D onto D. The Hardy number of D is the supremum of all p for which f belongs in the Hardy space H (D). A comb domain is the entire plane minus an infinite number of vertical rays symmetric with respect to the real axis. In this paper we prove that for any p ∈ [1,+∞], there is a comb domain with Hardy number equal to p and this result is sharp. It is known that the Hardy number is related with the moments of the exit time…

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