Multiple walsh series and Zygmund sets

Abstract

The classical Zygmund theorem claims that, for any sequence of positive numbers {ɛn} 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 {ɛn} 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.