Some Classes of L 1-Convergence of Fourier Series

In this paper equivalent classes of the classes M and S_pr, p > 1, > 0. r { 0,1,2, ... ,[]} defined by Shuyun [3] are obtained. Then, it is shown that the class S_pr, 1 > p 2, 0, r {0,1,2,...,[]} is a subclass of BVC_r, where S_pr is the equivalent class of the Shuyun's class S_pr, BV is the class of null sequences of bounded variation and C_r is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7].