Application of Cesàro summability methods of negative order to trigonometric Fourier series of summable and square summable functions

A Fourier series of a summable function is defined in the paper for which any sequence of Cesàro means of order $\alpha$ satisfying the inequality $-1<\alpha<0$ diverges on a set of positive measure.
A Fourier series of a square summable function is also defined that has the same property for $\alpha$ satisfying the inequality $-1<\alpha<-\frac12$.
Bibliography: 4 titles.