Arkiv för Matematik

Projections in the space H∞ and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces

Alexander Brudnyi

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Abstract

LetM be a non-compact connected Riemann surface of a finite type, and R⋐M be a relatively compact domain such that H1(M, Z)=H1(R, Z). Let $\tilde R \to R$ be a covering. We study the algebra H∞(U) of bounded holomorphic functions defined in certain subdomains $U \subset \tilde R$ . Our main result is a Forelli type theorem on projections in H∞(D).

Note

Research supported in part by NSERC.

Article information

Source
Ark. Mat., Volume 42, Number 1 (2004), 31-59.

Dates
Received: 2 December 2002
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898837

Digital Object Identifier
doi:10.1007/BF02432909

Mathematical Reviews number (MathSciNet)
MR2056544

Zentralblatt MATH identifier
1081.46032

Rights
2004 © Institut Mittag-Leffler

Citation

Brudnyi, Alexander. Projections in the space H ∞ and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces. Ark. Mat. 42 (2004), no. 1, 31--59. doi:10.1007/BF02432909. https://projecteuclid.org/euclid.afm/1485898837


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