第二类与Gamma函数有关的Hardy型不等式的等价条件

The Equivalent Conditions for a Second Kind of Hardy-Type Inequality Related to Gamma Function

引入恰当的参数,运用实分析方法以及权函数的技巧,获得2个与权函数估算及证明最佳常数因子有关的引理,并据此建立了几个关于带参数、最佳常数因子与Gamma函数有关的第二类非齐次核的Hardy型积分不等式的等价条件.同时,得到了几个关于第二类齐次核的Hardy型积分不等式的等价条件.

Two lemmas that are related to the estimate of weight function and the proving of best constant are obtained with the introduction of suitable parameters and the use of the way and techniques of real analysis and weight functions.On this basis,a few equivalent conditions for a second kind of Hardy-type integral inequality with a non-homogeneous kernel,related to a parameter and a best constant factor expressed in terms of Gamma function,are built.Meanwhile,some equivalent conditions for a second kind of Hardy-type integral inequality with the homogeneous kernel are deduced.