UNIFORM CONVERGENCE OF CES■RO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

In this paper we prove that if f∈C（[-π,π];）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.Ifα+β≥1/p, then there exists a continuous function f;of bounded partial p-variation on [-π,π];such that the Cesàro（C;-α,-β） meansσ;（f;;0, 0）of the double trigonometric Fourier series of f;diverge over cubes.