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A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces

A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on... AbstractThe 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 Hp{H_{p}}to the Lebesgue space Lp{L_{p}}for all 0<p≤1{0<p\leq 1}. We also prove that the result is sharp in a particular sense. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces

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Publisher
de Gruyter
Copyright
© 2019 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2018-0045
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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 Hp{H_{p}}to the Lebesgue space Lp{L_{p}}for all 0<p≤1{0<p\leq 1}. We also prove that the result is sharp in a particular sense.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Sep 1, 2019

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