On extreme points of the unit ball of a Hardy-Lorentz space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911061247000576 |
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| author | Astashkin, Sergey V. |
| author_facet | Astashkin, Sergey V. |
| contents | We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space $H(Λ(φ))$, posed by Semenov in 1978. New necessary and sufficient conditions, under which a normalized function $f$ in $H(Λ(φ))$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On extreme points of the unit ball of a Hardy-Lorentz space Astashkin, Sergey V. Functional Analysis 46E30, 30H10, 30J05, 46A55, 46B22 We investigate the problem of a characterization of extreme points of the unit ball of a Hardy-Lorentz space $H(Λ(φ))$, posed by Semenov in 1978. New necessary and sufficient conditions, under which a normalized function $f$ in $H(Λ(φ))$ 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. |
| title | On extreme points of the unit ball of a Hardy-Lorentz space |
| topic | Functional Analysis 46E30, 30H10, 30J05, 46A55, 46B22 |
| url | https://arxiv.org/abs/2507.12810 |