多重Fourier级数几乎处处收敛的判定──Marcinkiewicz判别法的一个推广

Test for Almost Everywhere Convergence of Multiple Fourier Seriers ──A Generalization of Marcinkiewicz's test

本文将单变量函数的Ｆｏｕｒｉｅｒ级数几乎处处收敛性的Ｍａｒｃｉｎｋｉｅｗｉｃｚ判别法推广到二维空间中一类集合──可测矩形上，给出了在可测矩形上，一个二元函数的Ｆｏｕｒｉｅｒ级数的矩形和几乎处处收敛的条件．

In the paper, Marcinkiewicz's test for almost everywhere convergence of Fourier seriesof one variable is generalized to the measurable rectangles in the twodimensional space. Asufficient condition of almost everywhere convergence of the rectangular sum of Fourier series of two variable on the measurable rectangles is given.