Summability of double Fourier series by Rogosinski-type means

Regularity conditions for Rogosinski-type(Bernstein-Rogosinsk-type) means were first introduced in the most general form by R.M.Trigub, Such means depend on some numerical parameters, an appropriate borelian measure and its support and a shape of a domain  generating partial sums of Fourier series. We investigate the case when the partial sums are generated by polygons ( a roctangle, a rhombus, symmetric with respect to an origin) and the mecasure is uniformly distributed over the areas of coreespondent polygons.