### Abstract

The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L ^{1} + L∞ and log^{+}-functions. In this paper we generalize Miyachi's theorem for R^{d} and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

Original language | English |
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Pages (from-to) | 551-558 |

Number of pages | 8 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 61 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Apr |

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### Keywords

- Chebli-Trimèche transform
- Dunkl transform
- Hardy's theorem
- Miyachi's theorem
- Radon transform

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Mathematical Society of Japan*,

*61*(2), 551-558. https://doi.org/10.2969/jmsj/06120551

**A generalization of Miyachi's theorem.** / Daher, Radouan; Kawazoe, Takeshi; Mejjaoli, Hatem.

Research output: Contribution to journal › Article

*Journal of the Mathematical Society of Japan*, vol. 61, no. 2, pp. 551-558. https://doi.org/10.2969/jmsj/06120551

}

TY - JOUR

T1 - A generalization of Miyachi's theorem

AU - Daher, Radouan

AU - Kawazoe, Takeshi

AU - Mejjaoli, Hatem

PY - 2009/4

Y1 - 2009/4

N2 - The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L 1 + L∞ and log+-functions. In this paper we generalize Miyachi's theorem for Rd and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

AB - The classical Hardy theorem on R, which asserts f and the Fourier transform of / cannot both be very small, was generalized by Miyachi in terms of L 1 + L∞ and log+-functions. In this paper we generalize Miyachi's theorem for Rd and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

KW - Chebli-Trimèche transform

KW - Dunkl transform

KW - Hardy's theorem

KW - Miyachi's theorem

KW - Radon transform

UR - http://www.scopus.com/inward/record.url?scp=67650976693&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650976693&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06120551

DO - 10.2969/jmsj/06120551

M3 - Article

AN - SCOPUS:67650976693

VL - 61

SP - 551

EP - 558

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -