双重三角级数的可积性定理

Integrability Theorems of Double Trigonometric Series

本文讨论了二元函数的可积性与其双重正弦、余弦级数的系数间的关系.将[1]中关于双重余弦的结果作了推广,同时得到了双重正弦级数的相应结果.并举例说明所得结果中指标不能再提高.

This note deals with the relations between the integrability of double trigonometric series and their coefficients. The corresponding results of [1]are extended to the double sine and cosine series. It is also shown by two examples that the indices are sharp.