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Abstract <p>We consider the problem of characterizing the set of extreme points of the unit ball in a Hardy–Lorentz space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9878_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\(H(\Lambda (\varphi ))\)</EquationSource> <!--DANMath2570003Astashkin-m1--> </InlineEquation>, posed by E.M. Semenov in 1978. New necessary and sufficient conditions under which a normalized function <i>f</i> in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9878_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\(H(\Lambda (\varphi ))\)</EquationSource> <!--DANMath2570003Astashkin-m2--> </InlineEquation> belongs to this set are found. The most complete results are obtained in the case when <i>f</i> is the product of an outer analytic function and a Blaschke factor.</p>

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On Some Class of Extreme Points of the Unit Ball of a Hardy–Lorentz Space

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • S. V. Astashkin

摘要

Abstract

We consider the problem of characterizing the set of extreme points of the unit ball in a Hardy–Lorentz space \(H(\Lambda (\varphi ))\) , posed by E.M. 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.