Fejer定理的一种多元推广

A Higher Dimensional Generalization of Fejér's Theorem

将一元傅立叶分析中关于傅氏级数及其共轭级数之间的收敛性关系的Ｆｅｊｅｒ定理推广到多元情形。主要结果为定理：若函数ｆ∈Ｌ（Ｅｋ）（ｋ≥２）的傅氏积分的球形平均σＲ（ｆ；ｘ）在域Ｄ内一致收敛，则它的共轭傅氏积分的球形平均σ↑￣Ｒ（ｆ；ｘ）在其（Ｃ，１）可和点处一定收敛。

In one-dimensional Fourier Analysis there are some results about the connection between convergence of Fourier series and that of its conjugate series such as Fejér's theorem and Kuttner's theorem.In this paper we discuss one of the higher dimensional analogues.