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A decomposition of functions with zero means on circles

Josip Globevnik Institute of Mathematics, Physics and Mechanics, University of Ljubljana

TBD mathscidoc:1701.333063

Arkiv for Matematik, 43, (2), 383-393, 2003.8
It is well known that every Hölder continuous function on the unit circle is the sum of two functions such that one of these functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. We prove that an analogue of this holds for Hölder continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole.
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@inproceedings{josip2003a,
  title={A decomposition of functions with zero means on circles},
  author={Josip Globevnik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203615051106872},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={2},
  pages={383-393},
  year={2003},
}
Josip Globevnik. A decomposition of functions with zero means on circles. 2003. Vol. 43. In Arkiv for Matematik. pp.383-393. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203615051106872.
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