均值有界变差条件及其在Fourier分析中的应用

摘要

This announcement is to raise an ultimate generalization to monotonicity condition on the Fourier (trigonometric) coefficient sequences. We prove this condition cannot be weak- ened any further to guarantee the uniform convergence of the sine series. Some interesting and important classical results in Fourier analysis are re-established under this ultimate condition. Over ninty year research history is surveyed in this announcement.The first original paper of this series of papers is posted in arXiv:math.CA/0611805 v1, November 27, 2006.