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
Uniform convergence of double trigonometric series
