Goginava, Ushangi Norm convergence of Fejér means of two-dimensional Walsh-Fourier series. (English) Zbl 1246.42023 Nawrocki, Marek (ed.) et al., Marcinkiewicz centenary volume. Proceedings of the Józef Marcinkiewicz centenary conference, June 28–July 2, 2010. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-14-0/pbk). Banach Center Publications 95, 317-324 (2011). It is known that the maximal operator \(\sigma^*\) of the two-dimensional Fejér means \(\sigma_{n,m}f\) of the Walsh-Fourier series is bounded from the Hardy space \(H_p\) to \(L_p\) if \(p>1/2\); see F. Weisz [Anal. Math. 22, No. 3, 229–242 (1996; Zbl 0866.42020)].In the paper under review it is proved that this is not true for \(p=1/2\), since there exists \(f\in H_{1/2}\) such that \(\sigma_{n,n}f\) is not uniformly bounded in weak \(L_{1/2}\).For the entire collection see [Zbl 1234.00021]. Reviewer: Ferenc Weisz (Budapest) MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Keywords:Walsh-Fourier series; Hardy spaces; maximal operator; martingales; Fejér means. Citations:Zbl 0866.42020 PDFBibTeX XMLCite \textit{U. Goginava}, Banach Cent. Publ. 95, 317--324 (2011; Zbl 1246.42023) Full Text: DOI