This allows us to identify the multiplier space of the mentioned Hardy type spaces as the space of bounded holomorphic functions on the domain. ******************************************************************************************
📌 3 Key Takeaways
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Objective & Hypothesis:We give a complete characterization of a certain class of Hardy type spaces on finitely connected planar domains.
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Key Findings & Data:In particular, we provide a decomposition result and give a description of such functions through their boundary values.
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Conclusion & Impact:This allows us to identify the multiplier space of the mentioned Hardy type spaces as the space of bounded holomorphic functions on the domain. ******************************************************************************************
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hardy space · decomposition · boundary values
Abstract
We give a complete characterization of a certain class of Hardy type spaces on finitely connected planar domains. In particular, we provide a decomposition result and give a description of such functions through their boundary values. As an application, we describe an isomorphism from the weighted Hardy space onto the classical Hardy-Smirnov space. This allows us to identify the multiplier space of the mentioned Hardy type spaces as the space of bounded holomorphic functions on the domain. ******************************************************************************************
Göğüş, N. G. (2020). Structure of weighted Hardy spaces on finitely connected domains. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 4. https://doi.org/10.15672/hujms.598004
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