On extreme points of the unit ball of a Hardy-Lorentz space

Sergey V. Astashkin

On extreme points of the unit ball of a Hardy-Lorentz space

Functional Analysis 2025-07-18 v1

Authors: Sergey V. Astashkin

Abstract

We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space $H(\Lambda(\varphi))$ , posed by Semenov in 1978. New necessary and sufficient conditions, under which a normalized function $f$ in $H(\Lambda(\varphi))$ belongs to this set, are found. The most complete results are obtained in the case when $f$ is the product of an outer analytic function and a Blaschke factor.

Keywords

Hardy-Lorentz space extreme points unit ball Blaschke factor outer analytic function

Cite

@article{arxiv.2507.12810,
  title  = {On extreme points of the unit ball of a Hardy-Lorentz space},
  author = {Sergey V. Astashkin},
  journal= {arXiv preprint arXiv:2507.12810},
  year   = {2025}
}

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32 pages

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