On holomorphic functions with cluster sets of finite linear measure

Published 21 Oct 2016 in math.CV | (1610.06964v1)

Abstract: We prove that if f is a holomorphic function on the open unit disc in C whose cluster set C(f) has finite linear measure and is such that the complement of C(f) has finitely many components, then the derivative of f belongs to the Hardy space H^1.

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