Scholarlink

<p>We derive a novel multidimensional Hilbert-type inequality incorporating a partial sum, by employing transfer formulas and the Hermite–Hadamard inequality. Unlike existing results, this new inequality features a kernel of the form <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mo>ln</mo> <mi>m</mi> <mo>+</mo> <msub> <mrow> <mo>∥</mo> <mi>v</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>∥</mo> </mrow> <mi>α</mi> </msub> <mo>)</mo> </mrow> <mi>β</mi> </msup> </mfrac> <mo stretchy="false">(</mo> <mi>β</mi> <mo>&gt;</mo> <mn>0</mn> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\frac{1}{\left ( \ln m+\left \Vert v(k)\right \Vert _{\alpha }\right ) ^{\beta }}( \beta &gt;0)$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>v</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$v(k)$</EquationSource> </InlineEquation> is a generalized internal variable. Moreover, we prove the optimality of the inequality under specific parameter conditions. Additionally, we discuss the equivalent formulation of the inequality and its operator expression. These results extend the applicability of Hilbert-type inequalities in multidimensional analysis.</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

A new multidimensional Hilbert-type inequality involving one partial sum

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月12日

查看全文
  • Xianyong Huang,
  • Bicheng Yang,
  • Bing He

摘要

We derive a novel multidimensional Hilbert-type inequality incorporating a partial sum, by employing transfer formulas and the Hermite–Hadamard inequality. Unlike existing results, this new inequality features a kernel of the form 1 ( ln m + ∥ v ( k ) ∥ α ) β ( β > 0 ) $\frac{1}{\left ( \ln m+\left \Vert v(k)\right \Vert _{\alpha }\right ) ^{\beta }}( \beta >0)$ , where v ( k ) $v(k)$ is a generalized internal variable. Moreover, we prove the optimality of the inequality under specific parameter conditions. Additionally, we discuss the equivalent formulation of the inequality and its operator expression. These results extend the applicability of Hilbert-type inequalities in multidimensional analysis.