### 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 H_{p(·)} to the variable Lebesgue space L_{p(·)}. Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from H_{p(·)} to L_{p(·)} and from the variable Hardy-Lorentz space H_{p(·),q} to the variable Lorentz space L_{p(·),q}. As a consequence, we can prove theorems about almost everywhere and norm convergence.

Original language | English |
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Pages (from-to) | 675-696 |

Number of pages | 22 |

Journal | Banach Journal of Mathematical Analysis |

Volume | 13 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### Keywords

- Boundedness
- Cesàro and Riesz maximal operator
- Cesàro means
- Riesz means
- Variable Hardy spaces
- Variable Hardy-Lorentz spaces

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory