On the divergence of the <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=45> means of double Walsh-Fourier series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the divergence of the means of double Walsh-Fourier series

Authors:	G Gá t

Institution:	Department of Mathematics, Bessenyei College, Nyíregyháza, P.O. Box 166., H--4400, Hungary

Abstract:	In 1992, Móricz, Schipp and Wade proved the a.e. convergence of the double means of the Walsh-Fourier series $\sigma _{n}f\to f$ ( $\min (n_{1}, n_{2})\to \infty , n=(n_{1},n_{2})\in {\mathbb{N}} ^{2}$ ) for functions in $L\text{log}^{+} L(I^{2})$ ( $I^{2}$ is the unit square). This paper aims to demonstrate the sharpness of this result. Namely, we prove that for all measurable function $\delta :0,+\infty ) \to 0,+\infty ) , \, \lim _{t\to \infty }\delta (t)=0$ we have a function such as $f\in L\text{log}^{+} L\delta (L)$ and $\sigma _{n}f$ does not converge to a.e. (in the Pringsheim sense).

Keywords:	Walsh group double $(C 1)$ means divergence

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