## Journal of the Mathematical Society of Japan

### A generalization of Miyachi's theorem

#### Abstract

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

#### Article information

Source
J. Math. Soc. Japan, Volume 61, Number 2 (2009), 551-558.

Dates
First available in Project Euclid: 13 May 2009

https://projecteuclid.org/euclid.jmsj/1242220721

Digital Object Identifier
doi:10.2969/jmsj/06120551

Mathematical Reviews number (MathSciNet)
MR2532900

Zentralblatt MATH identifier
1235.43008

#### Citation

DAHER, Radouan; KAWAZOE, Takeshi; MEJJAOLI, Hatem. A generalization of Miyachi's theorem. J. Math. Soc. Japan 61 (2009), no. 2, 551--558. doi:10.2969/jmsj/06120551. https://projecteuclid.org/euclid.jmsj/1242220721

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