Cesaro summation of fourier series of functions from multidimensional waterman classes

Results of Cesaro summation of Fourier series of functions from multidimensional Waterman classes are presented. Functions are assumed to be measurable and 2π-periodic in each variable, the Fourier series of functions are taken with respect to the trigonometric system, and the convergence of their rectangular partial sums is considered. It is shown that each fixed point, the Fourier series of f converges and the convergence is uniform on any interval lying inside the continuity interval of f. It is also found that at each regular point x, the Fourier series of f (x) converges to another Fourier series. For any function f from the class, its Fourier series is everywhere bounded and is uniformly bounded inside each continuity interval. For any function f from the class, its Fourier series is summable to another Fourier series at each regular point x0 and the summability is uniform on any compact set in the neighborhood of which the function is continuous.