On L 1 -convergence of Walsh-Fourier series

C. W. Onneweer

International Journal of Mathematics and Mathematical Sciences, 1978, vol. 1, 1-10

Abstract:

Let G denote the dyadic group, which has as its dual group the Walsh(-Paley) functions. In this paper we formulate a condition for functions in L 1 ( G ) which implies that their Walsh-Fourier series converges in L 1 ( G ) -norm. As a corollary we obtain a Dini-Lipschitz-type theorem for L 1 ( G ) convergence and we prove that the assumption on the L 1 ( G ) modulus of continuity in this theorem cannot be weakened. Similar results also hold for functions on the circle group T and their (trigonometric) Fourier series.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:373819

DOI: 10.1155/S016117127800006X

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