A curvilinear extension of Iversen-Tsuji’s theorem for simply connected domain

Abstract

Let D be a simply connected domain with at least two boundary points in the complex plane, and t a boundary point of D. For a meromorphic function f ( z ) f(z) in D, lim sup | f ( z ) | as z → t \lim \sup |f(z)|{\text {as}}\;z \to t is given in terms of accessible boundary points and prime ends. This gives a curvilinear extension of Iversen-Tsuji’s Theorem for a simply connected domain.