具广义单调系数三角级数的L~1-可积和L~1-收敛的充分必要条件

本文讨论了具有广义单调系数且满足条件ａｎｌｏｇｎ＝ｏ（１）（ｎ→），ｂｎｌｏｇｎ＝ｏ（１），（ｎ→ｏ）的一类三角级数的可积性和收敛性同时发生，同时，对于三角级数的阶典型平均Ｒｎ＝Ｒｎ（ｘ），我们还证明了，当三角级数的系数是广义单调数列时，），当且仅当，（ａｎ＋ｂｎ）ｌｏｇｎ＝ｏ（１），（ｎ→）。

Necessary and sufficicent conditions for L1-integrability andL1-convergence of a class of trigonometric series withgeneralized monotone coefficients

In this article , it is found that for a class of trigonometric series with general- ized monotone coefficients that satistfies anlogn =o (1 ) , (n- ) , bnlogn =o ( 1 ) , and (n) ,L1 integrability and L1-convergence occur together. Also , for the typical means of trigonometric series R(x) , it is proved that when coefficients of trigonometric series is a generalizd monotone sequence , S -R =0 ( 1 ) , if and only if (an bn) logn=0 (1).