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<p>In this paper, in order to study the B–P formula of weighted inframonogenic functions, two important lemmas are first given, which solve the difficulty caused by the non commutativity of Clifford valued functions in multiplication operations. Then, using the conclusion of the above lemmas and the relationship between &#xa0;<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="6_2025_1405_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{d}\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>d</mtext> <mi>σ</mi> </mrow> </math></EquationSource> </InlineEquation>&#xa0; under non-Euclidean distances and &#xa0;<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="6_2025_1405_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{d}\mu _{r}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>d</mtext> <msub> <mi>μ</mi> <mi>r</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>&#xa0; under Euclidean distances, the B–P formula for weighted inframonogenic functions is obtained by digging out singularities to satisfy the conditions for using the Stokes formula, and introducing new operators to simplify the calculation steps. Furthermore, the Cauchy integral formula for weighted inframonogenic functions is obtained.</p>

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The B–P Formula and Cauchy Integral Formula for Weighted Inframonogenic Functions\(\dag \)

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Ying Li,
  • Liping Wang,
  • Xin Jiang,
  • Xiaojia Yang

摘要

In this paper, in order to study the B–P formula of weighted inframonogenic functions, two important lemmas are first given, which solve the difficulty caused by the non commutativity of Clifford valued functions in multiplication operations. Then, using the conclusion of the above lemmas and the relationship between   \(\textrm{d}\sigma \) d σ   under non-Euclidean distances and   \(\textrm{d}\mu _{r}\) d μ r   under Euclidean distances, the B–P formula for weighted inframonogenic functions is obtained by digging out singularities to satisfy the conditions for using the Stokes formula, and introducing new operators to simplify the calculation steps. Furthermore, the Cauchy integral formula for weighted inframonogenic functions is obtained.