## Abstract

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Kaczmarz system is bounded from the dyadic Hardy-Lorentz space H_{pq} into the Lorentz space L_{pq} for every p > 1/2 and 0 < g ≤ ∞ provided that the supremum in the maximal operator is taken over special indices. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series for special indices with respect to the Walsh-Kaczmarz system. That is, σ_{2n} (f, x^{1}, x^{2}) → f(x^{1}, x^{2}) a.e. as n → ∞.

Original language | English |
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Pages (from-to) | 473-483 |

Number of pages | 11 |

Journal | Mathematical Inequalities and Applications |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 2006 |

Externally published | Yes |

## Keywords

- Marcinkiewicz-Fejér means
- Maximal operator
- Walsh-Kaczmarz system

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics

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