M. and S. Izumi  and the present author  have extended certain theorems of R.P. Boas  concerning
the Fourier coefficients of functions belonging to the Lipschitz classes. Very recently L. Leindler  has given further generalization using the so called quasi power-monotone sequences. The
goal of the present work is to further prove theorems similar to those of L. Leindler.
 R.P. BOAS Jr.,
Fourier series with positive coefficients, J.
Math. Anal. Appl., 17
 M. IZUMI and S.
IZUMI, Lipschitz classes and Fourier coefficients, J.
 L. LEINDLER, Power-monotone sequences and Fourier series
with positive coefficients, J. Inequal. Pure
Appl. Math., 1(1) (2000), Article 1, http://jipam.vu.edu.au/v1n1/001_99.html.
NEMETH, Fourier series with positive coefficients and
generalized Lipschitz classes, Math.
coefficients, modulus of
quasi power-monotone sequences.
2000 Mathematics Subject