Scholarlink

<p>We prove that an inner function has finite <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\cal L}(p)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">L</mi> </mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>-entropy if and only if its accumulated Möbius distortion is in <i>L</i><sup><i>p</i></sup>, 0 &lt; <i>p</i> &lt; ∞. We also study the support of the positive singular measures such that their corresponding singular inner functions have finite <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\cal L}(p)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">L</mi> </mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>-entropy.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Inner functions, Möbius distortion and angular derivatives

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月15日

查看全文
  • Konstantinos Bampouras,
  • Artur Nicolau

摘要

We prove that an inner function has finite \({\cal L}(p)\) L ( p ) -entropy if and only if its accumulated Möbius distortion is in Lp, 0 < p < ∞. We also study the support of the positive singular measures such that their corresponding singular inner functions have finite \({\cal L}(p)\) L ( p ) -entropy.