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<p>In this paper, we establish a normed fractional Faà di Bruno inequality within the framework of Lebesgue spaces. This extends the classical fractional chain rule from the range <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0&lt; s &lt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>s</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> to an arbitrarily large value of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(s\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>s</mi> </math></EquationSource> </InlineEquation>.</p>

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A Normed Fractional Chain Rule Counterpart to the Faà di Bruno Identity

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Sean Douglas

摘要

In this paper, we establish a normed fractional Faà di Bruno inequality within the framework of Lebesgue spaces. This extends the classical fractional chain rule from the range \(0< s < 1\) 0 < s < 1 to an arbitrarily large value of \(s\) s .