Properties of Cesàro Means of Double Fourier Series / D'yachenko A.M. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 2. P. 3-11 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 55-62].

The pointwise behavior of partial sums and Cesàro means of trigonometric series were studied in many papers. This paper deals with the behavior of rectangular Cesàro means at a point (x₀,y₀) for functions f(x,y) bounded in the square [-π; π]² and satisfying the condition

|f(x₀ + s, y₀ + t) - f(x₀, y₀)| ≤ ρ (√(s² + t²))^α, for some α ∈ (0,1) and all s and t.

Key words: Chesàro means, Fourier series.