Abstract:Let \({H^p}\left( \mathbb{D} \right)\) be the Hardy space of all holomorphic functions on the unit disk \(\mathbb{D}\) with exponent \(p>0\). If \(D\ne \mathbb{C}\) is a simply connected domain and \(f\) is the Riemann mapping from \(\mathbb{D}\) onto \(D\), then the Hardy number of \(D\), introduced by Hansen, is the supremum of all \(p\) for which \(f \in {H^p}\left( \mathbb{D} \right)\). Comb domains are a well-studied class of simply connected domains that, in general, have the form of the entire plane … Show more
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