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July 2019 Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces
Kristóf Szarvas, Ferenc Weisz
Banach J. Math. Anal. 13(3): 675-696 (July 2019). DOI: 10.1215/17358787-2018-0037

Abstract

We consider two types of maximal operators. We prove that, under some conditions, each maximal operator is bounded from the classical dyadic martingale Hardy space Hp to the classical Lebesgue space Lp and from the variable dyadic martingale Hardy space Hp() to the variable Lebesgue space Lp(). Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from Hp() to Lp() and from the variable Hardy–Lorentz space Hp(),q to the variable Lorentz space Lp(),q. As a consequence, we can prove theorems about almost everywhere and norm convergence.

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Kristóf Szarvas. Ferenc Weisz. "Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces." Banach J. Math. Anal. 13 (3) 675 - 696, July 2019. https://doi.org/10.1215/17358787-2018-0037

Information

Received: 27 June 2018; Accepted: 4 November 2018; Published: July 2019
First available in Project Euclid: 31 May 2019

zbMATH: 07083767
MathSciNet: MR3978943
Digital Object Identifier: 10.1215/17358787-2018-0037

Subjects:
Primary: 42B30
Secondary: 42C10 , 46E30 , 60G42 , 60G46

Keywords: boundedness , Cesàro and Riesz maximal operator , Cesàro means , Riesz means , variable Hardy spaces , variable Hardy–Lorentz spaces

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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