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).
Research supported in part by NSERC.
"Projections in the space H∞ and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces." Ark. Mat. 42 (1) 31 - 59, April 2004. https://doi.org/10.1007/BF02432909