### Abstract

We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space H_{p} to L_{p} if 1/2 <p <∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1, 1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L_{1} as n → ∞.

Original language | English |
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Pages (from-to) | 227-243 |

Number of pages | 17 |

Journal | Studia Mathematica |

Volume | 146 |

Issue number | 3 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Atomic decomposition
- Fejér means
- Hardy spaces
- Interpolation
- p-atom
- Spline systems

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Studia Mathematica*,

*146*(3), 227-243.

**On the Fejér means of bounded Ciesielski systems.** / Weisz, F.

Research output: Contribution to journal › Article

*Studia Mathematica*, vol. 146, no. 3, pp. 227-243.

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TY - JOUR

T1 - On the Fejér means of bounded Ciesielski systems

AU - Weisz, F.

PY - 2001

Y1 - 2001

N2 - We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space Hp to Lp if 1/2 1 as n → ∞.

AB - We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space Hp to Lp if 1/2 1 as n → ∞.

KW - Atomic decomposition

KW - Fejér means

KW - Hardy spaces

KW - Interpolation

KW - p-atom

KW - Spline systems

UR - http://www.scopus.com/inward/record.url?scp=0041025626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041025626&partnerID=8YFLogxK

M3 - Article

VL - 146

SP - 227

EP - 243

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 3

ER -