L1-Convergence of Double Trigonometric Series

In this paper we study the pointwise convergence and convergence in L-1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p, 0), (0, p) and (p, p) with the weight (jk)(P-1) for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of Moricz [6, 7] in the sense of higher values of p.