## Abstract

We prove that the Hausdorff operator generated by a function ∈ L^{1}(ℝ) is bounded on the real Hardy space H^{1}(ℝ). The proof is based on the closed graph theorem and on the fact that if a function f in L^{1} (ℝ) is such that its Fourier transform f̂(t) equals 0 for t < 0 (or for t > 0), then f ∈ H^{1}(ℝ).

Original language | English |
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Pages (from-to) | 1391-1396 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 128 |

Issue number | 5 |

DOIs | |

State | Published - 2000 |

## Keywords

- Cesàro operator
- Closed graph theorem
- Fourier transform
- Hausdorff operator
- Hubert transform
- Real hardy space H(ℝ)

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