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LetM be a non-compact connected Riemann surface of a finite type, andR⋐M be a relatively compact domain such thatH 1(M,Z)=H 1(R,Z). Let\(\tilde R \to R\) be a covering. We study the algebraH ∞(U) of bounded holomorphic functions defined in certain subdomains\(U \subset \tilde R\). Our main result is a Forelli type theorem on projections inH ∞(D).

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