Banach Journal of Mathematical Analysis

Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces

Kristóf Szarvas and Ferenc Weisz

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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.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 675-696.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1559268029

Digital Object Identifier
doi:10.1215/17358787-2018-0037

Mathematical Reviews number (MathSciNet)
MR3978943

Zentralblatt MATH identifier
07083767

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 60G42: Martingales with discrete parameter 60G46: Martingales and classical analysis 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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

Citation

Szarvas, Kristóf; Weisz, Ferenc. Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces. Banach J. Math. Anal. 13 (2019), no. 3, 675--696. doi:10.1215/17358787-2018-0037. https://projecteuclid.org/euclid.bjma/1559268029


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