一类半离散Hilbert型不等式的构造  

On the construction of a class of half-discrete Hilbert-type inequalities

作　　者：有名辉[1] YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China)

机构地区：[1]浙江机电职业技术学院数学教研室,浙江杭州310053

出　　处：《浙江大学学报（理学版）》2022年第4期422-426,共5页Journal of Zhejiang University（Science Edition）

基　　金：浙江机电职业技术学院科教融合孵化课题(A-0271-21-206)。

摘　　要：通过定义若干参量,构造了包含齐次及非齐次2种形态的半离散型核函数。借助正切函数的无穷级数表示和分析学方法,建立了用余切函数表示常数因子的半离散Hilbert型不等式,且证明了|α|^(-1/q)|β|^(-1/pπ)/γ[Φ(γπ/λ_(1))-Φ(γπ/λ_(2))]为最佳常数因子。通过对参量赋值,建立了特殊的齐次及非齐次Hilbert型不等式。By defining several parameters, a half-discrete kernel function including its homogeneous and nonhomogeneous forms is constructed. With the help of infinite series representation of tangent function and some techniques of analysis, a half-discrete Hilbert-type inequality with the constant factor expressed by cotangent function is established, and to prove that |α|^(-1/q)|β|^(-1/pπ)/γ[Φ(γπ/λ_(1))-Φ(γπ/λ_(2))] is the optimal constant factor. In addition, by assigning the parameters different values, some special homogeneous and non-homogeneous Hilbert-type inequalities are established.

关 键 词：HILBERT型不等式 无穷级数 余切函数 半离散 最佳常数因子 

分 类 号：O178[理学—数学]