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<p>This article determines the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2095_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell _p^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>ℓ</mi> <mi>p</mi> <mi>n</mi> </msubsup> </math></EquationSource> </InlineEquation> space and having values in the simply connected domain of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2095_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation>. Moreover, we investigate sharp Bohr radii for four distinct categories of holomorphic functions. These functions map the bounded balanced domain <i>G</i> of a complex Banach space <i>X</i> into the following domains: the right half-plane, the slit domain, the punctured unit disk, and the exterior of the closed unit disk.</p>

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Asymptotic value of the multidimensional Bohr radius

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Vibhuti Arora,
  • Shankey Kumar,
  • Saminathan Ponnusamy

摘要

This article determines the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the \(\ell _p^n\) ℓ p n space and having values in the simply connected domain of \(\mathbb {C}\) C . Moreover, we investigate sharp Bohr radii for four distinct categories of holomorphic functions. These functions map the bounded balanced domain G of a complex Banach space X into the following domains: the right half-plane, the slit domain, the punctured unit disk, and the exterior of the closed unit disk.