On the mean summability by Cesàro method of Fourier trigonometric series in two-weighted setting.
We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].