相关基金:Supported in part by Natural Science Foundation of China(No. 10471130). The work contained in this paper was done while the author was visiting 0saka City University, Japan, in March 2004, he thanks the Department of Mathematics of 0saka City University for its hospitality. Especially, the author thanks Professor T. Kamae for his hospitality and valuable discussions of the topic.
The present paper will give an essential generalization of Telyakovskii's results on the uniform convergence of trigonometric series with rarely changing coefficiets.