Approximation by double Walsh polynomials (Q1187576)

The author elegantly extends results of C. Watari (1963), S. Yano (1951), and S. L. Blyumin (1967) on the rate of approximation by partial sums of Walsh-Fourier series, their Cesàro and de la Vallée Poussin means, as well as saturation, from the univariate to multivariate cases. He considers explicitly the two-dimensional case for rectangular summation in \(L^ p(I^ 2)\), \(I^ 2= [0, 1)\times [0, 1)\), \(1\leq p\leq \infty\). He also raises three interesting problems. Background material can be found in a book by \textit{F. Schipp}, \textit{W. R. Wade} and \textit{P. Simon} [Walsh series (1990; Zbl 0727.42017)].