Almost everywhere convergence of Vilenkin-Fourier series

Gosselin, John

doi:10.1090/S0002-9947-1973-0352883-X

Almost everywhere convergence of Vilenkin-Fourier series
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Trans. Amer. Math. Soc. 185 (1973), 345-370 Request permission

Abstract:

It is shown that the partial sums of Vilenkin-Fourier series of functions in ${L^q}(G),q < 1$, converge almost everywhere, where G is a zero-dimensional, compact abelian group which satisfies the second axiom of countability and for which the dual group X has a certain bounded subgroup structure. This result includes, as special cases, the Walsh-Paley group ${2^w}$, local rings of integers, and countable products of cyclic groups for which the orders are uniformly bounded.

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