Volume 2,  Issue 2, 2001

Article 14



E-Mail: nemethj@math.u-szeged.hu

Received 25 July, 2000; accepted 10 August, 2000.
Communicated by: L. Leindler

ABSTRACT.   M. and S. Izumi [2] and the present author [7] have extended certain theorems of R.P. Boas [1] concerning the Fourier coefficients of functions belonging to the Lipschitz classes. Very recently L. Leindler [6] 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.

[1] R.P. BOAS Jr., Fourier series with positive coefficients, J. Math. Anal. Appl., 17 (1967), 463–483.
[2] M. IZUMI
and S. IZUMI, Lipschitz classes and Fourier coefficients, J. Math. Mech., 18 (1969), 857–870.
[6] 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.
[7] J. NEMETH, Fourier series with positive coefficients and generalized Lipschitz classes, Math. 54 (1990), 291–304.

Key words:
Fourier series, Fourier coefficients, modulus of continuity, quasi power-monotone sequences.

2000 Mathematics Subject Classification:
26A16, 26A15, 40A05.

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