The Corona theorem for Denjoy domains
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Publication:1066311
DOI10.1007/BF02392536zbMath0578.30043OpenAlexW2024457796MaRDI QIDQ1066311
Peter W. Jones, John B. Garnett
Publication date: 1985
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392536
Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of bounded analytic functions of one complex variable (30H05) Ideals, maximal ideals, boundaries (46J20)
Related Items (26)
Ideals of bounded holomorphic functions on simple n-sheeted discs ⋮ Interpolating sequences on plane domains ⋮ Gromov hyperbolicity of Denjoy domains ⋮ A new approach to the corona theorem for domains bounded by a C^1+α curve ⋮ Constructing continuous functions holomorphic to a curve ⋮ Limits on an extension of Carleson's \(\bar\partial\)-theorem ⋮ On the corona problem for strongly pseudoconvex domains ⋮ The corona problem with restrictions on the relative position of sublevel sets ⋮ \(L^\infty\) Estimates for the Banach-valued \(\bar{\partial}\)-problem in a disk ⋮ A short proof of Hara and Nakai’s theorem ⋮ Positive harmonic functions on Denjoy domains in the complex plane ⋮ A real variable characterization of Gromov hyperbolicity of flute surfaces ⋮ Extension of matrices with entries in $H^{\infty }$ on coverings of Riemann surfaces of finite type ⋮ Approximating Continuous Functions by Holomorphic and Harmonic Functions ⋮ The corona problem with two pieces of data ⋮ The Corona Theorem for Domains whose Boundary Lies in a Smooth Curve ⋮ Corona theorem for \(H^{\infty }\) on covering of Riemann surfaces of finite type ⋮ Approximation by ratios of bounded analytic functions ⋮ The Corona theorem on the complement of certain square Cantor sets ⋮ On the corona theorem on smooth curves ⋮ A new construction of Riemann surfaces with corona ⋮ Comparative Gromov hyperbolicity results for the hyperbolic and quasihyperbolic metrics ⋮ Location of geodesics and isoperimetric inequalities in Denjoy domains ⋮ Valuations on Meromorphic Functions of Bounded Type ⋮ Corona Problem for H ∞ on Riemann Surfaces ⋮ Martin boundaries of sectorial domains
Cites Work
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- \(L^\infty\) estimates for the \(\bar\partial\) problem in a half-plane
- Critical points of Green's function, harmonic measure, and the corona problem
- Interpolating sequences and the Shilov boundary of \(H^\infty(\Delta)\)
- Interpolating sequences and separation properties
- Bounded analytic functions and Gleason parts
- Localization of the corona problem
- Analytic capacity and measure
- Interpolations by bounded analytic functions and the corona problem
- Confromal invariants and function-theoretic null-sets
- An Interpolation Problem for Bounded Analytic Functions
- Generators for some rings of analytic functions
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