Abstract
We consider the single cosine series with nonnegative coefficients. The estimates of the integral of the function phi of the single cosine series times x with power alpha-1, alpha is areal number and phi belongs to delta(p,q) for p>1 and p no less then q greater then 0 .Our results generalize a result of Boas . 2.Preliminaries………………… ……………...3 3.Main Results…………………………………...7 4.Comments.………….……………………………12 References….………… …………………………13