Nagy, Károly Approximation by Nörlund means of double Walsh-Fourier series for Lipschitz functions. (English) Zbl 1243.42038 Math. Inequal. Appl. 15, No. 2, 301-322 (2012). The Nörlund means of rectangular partial sums of a double Walsh-Fourier series are defined by \[ T_{m,n}\left( f;x^{1},x^{2}\right) :=\frac{1}{Q_{m,n}}\sum_{j=0}^{m} \sum_{k=0}^{n}q_{m-j,n-k}S_{j,k}\left( f;x^{1},x^{2}\right) , \] where \[ Q_{m,n}:=\sum_{j=0}^{m}\sum_{k=0}^{n}q_{j,k}. \] 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 \(L_{p},1\leq p\leq \infty \).Earlier results on one-dimensional Nörlund means of the Walsh-Fourier series were given by F. Móricz and A. H. Siddiqi [J. Approximation Theory 70, No. 3, 375–389 (1992; Zbl 0757.42009)]. Reviewer: Ushangi Goginava (Tbilisi) Cited in 1 ReviewCited in 15 Documents MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42B08 Summability in several variables Keywords:Walsh group; Walsh system; Nörlund means Citations:Zbl 0757.42009 PDFBibTeX XMLCite \textit{K. Nagy}, Math. Inequal. Appl. 15, No. 2, 301--322 (2012; Zbl 1243.42038) Full Text: DOI