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On the uniform convergence and L¹-convergence of double Walsh-Fourier series

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Móricz F.

Studia Mathematica

1992

tom 102

nr 3

225-237

In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in $L^p$-norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by $L^p$ we mean $C_W$, the collection of uniformly W-continuous functions f(x, y), endowed with the supremum norm. As special cases, we obtain the extensions of the Dini-Lipschitz test and the Dirichlet-Jordan test for double Walsh-Fourier series.

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1 Studia Mathematica

1 Móricz F.

1 1992

Wyniki wyszukiwania

On the uniform convergence and L¹-convergence of double Walsh-Fourier series