Scholarlink

<p>By giving a series of estimates of multiplication operators, investigating Cauchy transforms and using <i>L</i><sup>2</sup>-bounded Calderón–Zygmund operators, we provide the corona theorem with countably many functions for multiplier algebras of weighted Dirichlet spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\cal D}_{K}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mi mathvariant="script">D</mi> </mrow> <mrow> <mi>K</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. Our result thereby gives an extension of a corona theorem with infinitely many functions from the Dirichlet space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\cal D}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mi mathvariant="script">D</mi> </mrow> </math></EquationSource> </InlineEquation> to a weighted Dirichlet space <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\cal D}_{K}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mi mathvariant="script">D</mi> </mrow> <mrow> <mi>K</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> for a general weight function <i>K</i>.</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

The Corona Theorem with Countably Many Functions for Multiplier Algebras of Weighted Dirichlet Spaces

  • 期刊论文

  • 发表日期：

    2025年10月15日

查看全文
  • Weiye Pan,
  • Hasi Wulan

摘要

By giving a series of estimates of multiplication operators, investigating Cauchy transforms and using L2-bounded Calderón–Zygmund operators, we provide the corona theorem with countably many functions for multiplier algebras of weighted Dirichlet spaces \({\cal D}_{K}\) D K . Our result thereby gives an extension of a corona theorem with infinitely many functions from the Dirichlet space \({\cal D}\) D to a weighted Dirichlet space \({\cal D}_{K}\) D K for a general weight function K.