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

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).