在MVBVF条件下的加权可积性

Weighted Integrability under MVBVF Condition

将系数数列的MVBV条件推广到函数的MVBV条件,分别给出了MVBV条件下正弦积分与余弦积分加权可积的充分必要条件,并利用Cauchy收敛准则、分部积分和适当放缩等数学方法进行证明,从而进一步完善了三角级数可积性的理论。

This paper generalizes MVBV condition of coefficient series to MVBV condition of function, gives sufficient and necessary condition of sine integral and cosine integral under MVBV condition respectively, and utilizes Cauchy convergence criterion, integration by parts, suitable scaling and other mathematical methods for confirmation so as to further perfect the integrability theory of trigonometric series.