一个含多参数混合核的Hilbert型积分不等式及应用

摘要

引入双共轭指数对,利用权函数和实分析方法,建立了一个含多参数混合核的Hilbert型积分不等式和它的等价式,证明了它们的常数因子是最佳值,并浅谈了其应用,得到一系列特殊且有意义的结果.%By introducing two conjugate indexes and using the way of weight coefficient and the method of real analysis, a Hilbert-type integral inequality with the mixed kernel of some parameters and its equivalent form are given. Their constant factor is proved to be the best possible, and its application is discussed. A series of special and meaningful results are obtained.