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On an Estimate of the Partial Sums of Vilenkin-Fourier
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].
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- Research Article
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- Copyright © Canadian Mathematical Society 1991
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