On a Hilbert-Type Integral Operator with the None-Homogeneous Kernel

Y. Bi-cheng
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Abstract

In this paper,by using the way of weight function and the technic of real analysis and functional analysis,a Hilbert-type integral operator T with the none-homogeneous kernel is defined, and the norm is obtained.As applications,two equivalent inequalities related with the norm are given,the reverse forms and some particular cases with the best constant factors are considered.
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具有非齐次核的hilbert型积分算子
本文利用权函数的方法,利用实分析和泛函分析的技术,定义了一个具有非齐次核的hilbert型积分算子T,并得到了其范数。作为应用,给出了两个与范数相关的等价不等式,并考虑了其相反形式和具有最佳常数因子的一些特殊情况。
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