Feng, Lei et al., Trigonometric series with a generalized monotonicity condition, Acta mathematica Sinica. English series (Print) , 30(8), 2014, pp. 1289-1296
In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.