Properties of Cesàro means of double Fourier series

The pointwise behavior of partial sums and Chesaro means of trigonometric series were studied in many papers. This article deals with behavior of rectangular Chesaro means at a point $(x_0,y_0)$ for functions $f(x,y)$ bounded on square the $[-\pi;\pi]^2$ and satisfying the condition $|f(x_0+s,y_0+t)-f(x_0,y_0)|\le\rho(\sqrt{s^2+t^2})^\alpha$, for some $\alpha\in(0,1)$ and all $s$ and $t$.