一个新的零齐次核的Hilbert型积分不等式及其等价形式

A New Hilbert-Type Integral Inequality with the Homogeneous Kernel of 0-Degree and Equivalent Form

零齐次核的Hilbert型积分不等式是分析学及相关领域的重要不等式,本文通过对权函数的估算,应用实分析的技巧,建立了一个核为e-β(y/x)n的新零齐次核的Hilbert型积分不等式及其等价形式,且具有最佳常数因子,推广了有关文献结果.

Hilbert-type integral inequality with the homogeneous kernel of O-degree is an important inequality in analytic and related fields. In this paper, by estimating the weight function, using the real analysis, we give a new Hilbert-type integral inequality with homogeneous kernel of O-degree , the kernel is e-β（y/x）n , and the constant factor is the best, extended results.