On an Estimate of the Partial Sums of Vilenkin-Fourier
Keyword(s):
AbstractWe 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].
2014 ◽
Vol 285
(1)
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pp. 34-55
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Convergence and localization in Orlicz classes for multiple Walsh–Fourier series with a lacunary sequence of rectangular partial sums
2016 ◽
Vol 435
(1)
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pp. 765-782