English

On holomorphic functions with cluster sets of finite linear measure

Complex Variables 2016-10-25 v1

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.

Keywords

Cite

@article{arxiv.1610.06964,
  title  = {On holomorphic functions with cluster sets of finite linear measure},
  author = {Josip Globevnik and David Kalaj},
  journal= {arXiv preprint arXiv:1610.06964},
  year   = {2016}
}

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6 pages