Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 41837, 15 pages

On the mean summability by Cesaro method of Fourier trigonometric series in two-weighted setting

A. Guven1 and V. Kokilashvili2

1Department of Mathematics, Faculty of Art and Science, Balikesir University, Balikesir 10145, Turkey
2International Black Sea University, Tbilisi 0131, Georgia

Received 26 June 2005; Revised 19 October 2005; Accepted 23 October 2005

Copyright © 2006 A. Guven and V. Kokilashvili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Cesaro summability of trigonometric Fourier series is investigated in the weighted Lebesgue spaces in a two-weight case, for one and two dimensions. These results are applied to the prove of two-weighted Bernstein's inequalities for trigonometric polynomials of one and two variables.