تقرير
On the set of extreme points of the unit ball of a Hardy-Lorentz space
| العنوان: | On the set of extreme points of the unit ball of a Hardy-Lorentz space |
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| المؤلفون: | Astashkin, Sergey V. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 46E30, 30H10, 30J05, 46A55, 46B22 |
| الوصف: | We prove that every measurable function $f:\,[0,a]\to\mathbb{C}$ such that $|f|=1$ a.e. on $[0,a]$ is an extreme point of the unit ball of the Lorentz space $\Lambda(\varphi)$ on $[0,a]$ whenever $\varphi$ is a not linear, strictly increasing, concave, continuous function on $[0,a]$ with $\varphi(0)=0$. As a consequence, we complement the classical de Leeuw-Rudin theorem on a description of extreme points of the unit ball of $H^1$ showing that $H^1$ is a unique Hardy-Lorentz space $H(\Lambda(\varphi))$, for which every extreme point of the unit ball is a normed outer function. Moreover, assuming that $\varphi$ is strictly increasing and strictly concave, we prove that every function $f\in H(\Lambda(\varphi))$, $\|f\|_{H(\Lambda(\varphi))}=1$, such that the absolute value of its nontangential limit ${f}(e^{it})$ is a constant on some set of positive measure of $[0,2\pi]$, is an extreme point of the unit ball of $H(\Lambda(\varphi))$. Comment: submitted |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.10178 |
| رقم الأكسشن: | edsarx.2407.10178 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |