In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） ...In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） summable （α＋β 〈 1/p,α,β 〉 0） in the sense of Pringsheim. If α ＋ β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro （C;-α,-β） means σn,m^-α,-β（f0;0,0） of the double trigonometric Fourier series of f0 diverge over cubes.展开更多
文摘In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） summable （α＋β 〈 1/p,α,β 〉 0） in the sense of Pringsheim. If α ＋ β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro （C;-α,-β） means σn,m^-α,-β（f0;0,0） of the double trigonometric Fourier series of f0 diverge over cubes.
