BMO Functions as Harmonic Sections of Flat Bundles on the Maximal Ideal Space of H ?/sup>

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• 作者：Alexander Brudnyi
• 关键词：Primary 30H35 ; Secondary 30H05 ; BMO function ; maximal ideal space of $${H^\infty(\mathbb D)}$$ H ? D ) ; flat principal bundle
• 刊名：Integral Equations and Operator Theory
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：83
• 期：1
• 页码：61-72
• 全文大小：501 KB
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• 作者单位：Alexander Brudnyi (1)
  
  1. Department of Mathematics and Statistics, University of Calgary, Calgary, AB, 2N 1N4, Canada
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

We obtain a characterization of BMOH functions in terms of their approximation by locally constant functions. Also, we show that there is a natural correspondence between spaces of BMO functions and of harmonic sections of principal flat bundles with fibre \({\mathbb{R}}\) on the maximal ideal space \({\mathcal{M}}\) of the Banach algebra \({H^\infty(\mathbb{D})}\) of bounded holomorphic functions on the open unit disk \({\mathbb{D}\subset\mathbb{C}}\). Keywords BMO function maximal ideal space of \({H^\infty(\mathbb D)}\) flat principal bundle