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

  • István Blahota , Karoly Nagy , Lars-Erik Persson and George Tephnadze EMAIL logo
Published/Copyright: September 20, 2018
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Abstract

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 Hp to the Lebesgue space Lp for all 0<p1. We also prove that the result is sharp in a particular sense.

MSC 2010: 42C10; 42B25

Award Identifier / Grant number: DI/9/5-100/13

Award Identifier / Grant number: DO/24/5-100/14

Award Identifier / Grant number: YS15-2.1.1-47

Funding statement: Research was supported by project TÁMOP-4.2.2.A-11/1/KONV-2012-0051, by Shota Rustaveli National Science Foundation grants DI/9/5-100/13, DO/24/5-100/14, YS15-2.1.1-47 and by a Swedish Institute scholarship no. 10374-2015.

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Received: 2016-02-28
Revised: 2017-02-04
Accepted: 2017-03-16
Published Online: 2018-09-20
Published in Print: 2019-09-01

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