The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and ...The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence （γ-PBVS）.展开更多
基金Supported by the National Science Foundation of China(60970151,70973110)the Natural Science Foundation of Zhejiang Province(Y7080068)the Professor Foundation of Zhejiang Gongshang University(07-13)
文摘The inequality sup n≥1｜n∑k=1 sinkx/k｜≤3√π,plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence （γ-PBVS）.
