Convergence of doublecosine series

Abstract

In this paper we consider double cosine 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 p > 1. We study pointwise convergence, uniform convergence and convergence in L r -norm of the series under consideration. In a certain sense our results extend the results of Young [7], Kolmogorov [3] and Móricz [4, 5].