### Abstract

We investigate the Kronecker product of bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system from the Haar system. It is shown that the maximal operator of the Fejér means of the d-dimensional Ciesielski-Fourier series is bounded from the Hardy space H_{p}([0, 1)^{d}_{1}×...×[0,1)^{dl} to L_{p} ([0, 1)^{d}) if 1/2 < p < ∞ and m_{j} ≥0, {pipe}k_{j}{pipe} ≤ m_{j}+1. By an interpolation theorem, we get that the maximal operator is also of weak type H_{1}^{#i}, L_{1} (i=1,...,l), where the Hardy space H_{1}^{#i} is defined by a hybrid maximal function and H_{1}^{#i} ⊃ L(log L)^{l-1}. As a consequence, we obtain that the Fejér means of the Ciesielski-Fourier series of a function f converge to f a.e. if f ∈ H_{1}^{#i} and converge in a cone if fεL_{1}.

Original language | English |
---|---|

Pages (from-to) | 135-155 |

Number of pages | 21 |

Journal | Analysis Mathematica |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2002 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)