Regularity and approximation properties of Bernstein-Rogosinski type means of double Fourier series (Q1078457)

In analogy with the one-dimensional Rogosinski-Bernstein means one can introduce generalized Rogosinski-Bernstein means of periodic functions of two variables in the form \[ R_ n(f;x,y)=\int_{R^ 2}S_ n(f,W_ 0,x-\frac{\gamma u}{n},y-\frac{\gamma v}{n})d\quad \mu (u,v) \] where \(S_ n(f,W_ 0,x,y)\) are the partial sums of the Fourier series corresponding to the regions \(nW_ 0\) and \(d\mu\) is some Borel measure on \(R^ 2\). The author investigates the regularity of these means and in two dimension their approximation properties.