In this paper equivalent classes of the classes M'
α and S'
p
α
r, p >1, α≥0,r ∈{0,1,2,...,[α]} defined by Sheng [5] are obtained. Then it is shown that the classes of Fourier coefficients S
p, S'
p(case r=α=0) and S
p(δ), p>1, defined by Č. V. Stanojević, V. B. Stanojević Sheng and the author of the present note are identical. As a corollary of this result, the L
1-estimate for cosine series, obt...... hiện toàn bộ