Hardy Number of Koenigs Domains: Sharp Estimate
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis, Rodr\'iguez-Piazza

TL;DR
This paper establishes a sharp lower bound of 1/2 for the Hardy number of regular Koenigs domains, indicating the integrability properties of holomorphic functions mapping the unit disc into these domains.
Contribution
It provides the first sharp estimate for the Hardy number of Koenigs domains, advancing understanding of their boundary behavior and function theory.
Findings
Hardy number of Koenigs domains is at least 1/2
Holomorphic functions into these domains are in all Hardy spaces H^p for p<1/2
The estimate is sharp, confirming the bound cannot be improved
Abstract
Let be a regular Koenigs domain in the complex plane . We prove that the Hardy number of is greater or equal to . That is, every holomorphic function in the unit disc belongs to the Hardy space for all .
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Holomorphic and Operator Theory · Algebraic and Geometric Analysis
