摘要
证明了重组数的经典Hilbert重不等式通过引入一个适当的形如π－θ／（θ＞0）的权函数可以把两个单独的和都得到改进。借助于Euler—Maclaurin求和公式得到了一个非常强的结果。
It is shown that the classical Hilbert inequality for double seies can be refined by introducing aproper weight function of the form π-θ/(with θ>1) into either of the two single summations. A quitesharp result is attained by the aid of Euler-Maclaurin summation formula for certain infinite series involved.
基金
国家自然科学基金
