Browsing Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag) by Author "Blahota, Istvan"
A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces Blahota, Istvan; Nagy, Karoly; Persson, Lars Erik; Tephnadze, George (Journal article; Peer reviewed, 2018-09-20)The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense.
Blahota, Istvan; Persson, Lars Erik; Tephnadze, G (Journal article; Peer reviewed; Tidsskriftartikkel, 2017-03-13)In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H 1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.