On the order of rational Fourier coefficients of various bounded variations

Abstract

In this article, we will estimate the order of rational Fourier coefficients of functions of various bounded variations. If f is a function on R of bounded variation and period 2π, then its nth rational Fourier coefficients c _n (f) = O(1/2n). These results are extended to certain other classes of functions of generalized variations such as p-bounded variation and Φ-bounded variation.

Keywords:

• rational Fourier coefficient
• functions of p-bounded variation
• Φ-bounded variation
• Λ-bounded variation
• Φ–Λ-bounded variation

Acknowledgements

This research is supported by NSFC (11101094), NSF of Guangdong (s201104000389) and FDYT(LYM10071).