On the uniform convergence and L¹-convergence of double Walsh-Fourier series
Móricz, Ferenc
Studia Mathematica, Tome 103 (1992), p. 225-237 / Harvested from The Polish Digital Mathematics Library
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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 Lp-norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by Lp we mean CW, 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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:215925 
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Móricz, Ferenc. On the uniform convergence and L¹-convergence of double Walsh-Fourier series. Studia Mathematica, Tome 103 (1992) pp. 225-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p225bwm/

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