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

Abstract

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. Copyright (C) 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.