In this paper equivalent classes of the classes
M''
and
S''
p
r,
p >1,
0,r
{0,1,2,...,[
]} defined by Sheng [5] are obtained. Then it is shown that the classes of Fourier coefficients
S
p,
S''
p(case
r=
=0) and
S
p(
),
p>1, defined by
. V. Stanojevi
, V. B. Stanojevi
Sheng and the author of the present note are identical. As a corollary of this result, the
L
1-estimate for cosine series, obtained in [10], is refined.