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.
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}
}
Comments
6 pages