Approximation by Nörlund means of double Walsh-Fourier series for Lipschitz functions
The Nörlund means of rectangular partial sums of a double Walsh-Fourier series are defined by NEWLINE\[NEWLINE T_{m,n}\left( f;x^{1},x^{2}\right) :=\frac{1}{Q_{m,n}}\sum_{j=0}^{m} \sum_{k=0}^{n}q_{m-j,n-k}S_{j,k}\left( f;x^{1},x^{2}\right) , NEWLINE\]NEWLINE where NEWLINE\[NEWLINE Q_{m,n}:=\sum_{j=0}^{m}\sum_{k=0}^{n}q_{j,k}. NEWLINE\]NEWLINE The main aim of this paper is to investigate the rate of approximation by the Nörlund means \(T_{m,n}\left( f;x^{1},x^{2}\right) \) the double Walsh-Fourier series of a function in \(L_{p},1\leq p\leq \infty \).NEWLINENEWLINEEarlier results on one-dimensional Nörlund means of the Walsh-Fourier series were given by \textit{F. Móricz} and \textit{A. H. Siddiqi} [J. Approximation Theory 70, No. 3, 375--389 (1992; Zbl 0757.42009)].
scientific article; zbMATH DE number 6037637