## Banach Journal of Mathematical Analysis

### Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces

#### 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 $H_{p}$ to the classical Lebesgue space $L_{p}$ and from the variable dyadic martingale Hardy space $H_{p(\cdot )}$ to the variable Lebesgue space $L_{p(\cdot )}$. Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from $H_{p(\cdot )}$ to $L_{p(\cdot )}$ and from the variable Hardy–Lorentz space $H_{p(\cdot ),q}$ to the variable Lorentz space $L_{p(\cdot ),q}$. 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

#### 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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