Double trigonometric series with coefficients of bounded variation of higher order

Abstract

In this paper the following convergence properties are established for the rectangular partial sums of the double trigonometric series, whose coefficients form a null sequence of bounded variation of order $ (p,0) $, $ (0,p) $ and $ (p,p) $, for some $ p\ge 1$: (a) pointwise convergence; (b) uniform convergence; (c) $ L^r $-integrability and $ L^r $-metric convergence for $ 0<{1\over p}$. Our results extend those of Chen [2, 4, 5] and M'oricz [7, 8, 9] and Stanojevic [10].