A generalization of Miyachi's theorem

Radouan Daher, Takeshi Kawazoe, Hatem Mejjaoli

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 Rd and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.

Original languageEnglish
Pages (from-to)551-558
Number of pages8
JournalJournal of the Mathematical Society of Japan
Volume61
Issue number2
DOIs
Publication statusPublished - 2009 Apr

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Hardy's Theorem
Dunkl Transform
Generalized Fourier Transform
Fourier transform
Generalise
Theorem
Generalization

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Journal of the Mathematical Society of Japan, Vol. 61, No. 2, 04.2009, p. 551-558.

Research output: Contribution to journalArticle

Daher, Radouan ; Kawazoe, Takeshi ; Mejjaoli, Hatem. / A generalization of Miyachi's theorem. In: Journal of the Mathematical Society of Japan. 2009 ; Vol. 61, No. 2. pp. 551-558.
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