| 摘要: | Consider the double trigonometric series whose coefficients satisfy conditions of bounded variation of order (p, 0), (0, p), and (p, p) with the weight ((j) over bar (k) over bar)(p-1) for some p > 1. The following properties concerning the rectangular partial sums of this series are obtained: (a) regular convergence; (b) uniform convergence; (c) weighted L-r-integrability and weighted LT-convergence; and (d) Parseval's formula. Our results generalize Bary [1, p. 656], Boas [2, 3], Chen [6, 7], Kolmogorov [9], Marzug [10], Moricz [11, 12, 13, 14], Ul'janov [15], Young [16], and Zygmund [17, p. 4]. |
