L1-CONVERGENCE OF DOUBLE TRIGONOMETRIC SERIES

Abstract

In this paper we study the pointwise convergence and convergence
in L1-norm of double trigonometric series whose coecients form a
null sequence of bounded variation of order (p; 0); (0; p) and (p; p) with
the weight (jk)p????1 for some 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