On holomorphic functions with cluster sets of finite linear measure

Josip Globevnik; David Kalaj

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arXiv · 1610.06964

On holomorphic functions with cluster sets of finite linear measure

Josip Globevnik·David Kalaj

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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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Josip Globevnik, David Kalaj. 2016-10-21. On holomorphic functions with cluster sets of finite linear measure. https://arxiv.org/abs/1610.06964

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