On uniformly convergent double Fourier series

The uniform convergence of the partial sums, relative to a system of homothetic starlike polygons, is considered. Among other things, it is established an arbitrary preassigned positive sequence from can be majorized by the coefficients of a uniformly convergent double Fourier series.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 151–162, 1989.