Multiple walsh series and Zygmund sets

The classical Zygmund theorem claims that, for any sequence of positive numbers {? _n } monotonically tending to zero and any δ > 0, there exists a set of uniqueness for the class of trigonometric serieswhose coefficients aremajorized by the sequence {? _n } whosemeasure is greater than 2π ?δ. In this paper, we prove the analog of Zygmund’s theorem for multiple series in the Walsh system on whose coefficients rather weak constraints are imposed.