Journal of the Mathematical Society of Japan

A generalization of Miyachi's theorem

Radouan DAHER, Takeshi KAWAZOE, and Hatem MEJJAOLI

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Abstract

The classical Hardy theorem on R, which asserts f and the Fourier transform of f cannot both be very small, was generalized by Miyachi in terms of L1+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.

Article information

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

Dates
First available in Project Euclid: 13 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1242220721

Digital Object Identifier
doi:10.2969/jmsj/06120551

Mathematical Reviews number (MathSciNet)
MR2532900

Zentralblatt MATH identifier
1235.43008

Subjects
Primary: 43A85: Analysis on homogeneous spaces
Secondary: 43A62: Hypergroups 43A32: Other transforms and operators of Fourier type 44A12: Radon transform [See also 92C55] 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Hardy's theorem Miyachi's theorem Radon transform Dunkl transform Chébli-Trimèche transform

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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