Double Walsh Series with Coefficients of Bounded Variation

Abstract

Convergence properties of double Walsh series are studied whose coefficients form a null sequence of bounded variation. These series converge regularly at all points of (0, 1) x (0, 1) and converge in the pseudometric of $L^r$ for all $r\in (0,1)$. Sufficient conditions for convergence are also proved which involve the second-order differences of the coefficients.