\(BMO\) functions as harmonic sections of flat bundles on the maximal ideal space of \(H^\infty\)

DOI10.1007/s00020-014-2211-4zbMath1333.30070OpenAlexW2077320370MaRDI QIDQ747180

Alexander Brudnyi

Publication date: 23 October 2015

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-014-2211-4

zbMATH Keywords

harmonic functionsmaximal ideal spaceBMO functionsbounded holomorphic functionsflat principal bundle

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of bounded analytic functions of one complex variable (30H05) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Ideals, maximal ideals, boundaries (46J20) BMO-spaces (30H35)

Related Items (1)

Oka principle on the maximal ideal space of $\boldsymbol {H^\infty }$

Cites Work

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• Banach-valued holomorphic functions on the maximal ideal space of \(H ^{\infty }\)
• Čech cohomology and covering dimension for the \(H^ \infty\) maximal ideal space
• Holomorphic Banach vector bundles on the maximal ideal space of \(H^\infty\) and the operator corona problem of Sz.-Nagy
• On the completion problem for algebra \(H^{\infty}\)
• \(H^p\) spaces of several variables
• Interpolations by bounded analytic functions and the corona problem
• Some characterizations of 𝐶(ℳ)
• Characterizations of bounded mean oscillation

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