A generalization of Miyachi’s theorem

Radouan DAHER; Takeshi KAWAZOE; Hatem MEJJAOLI

doi:10.2969/jmsj/06120551

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

A generalization of Miyachi’s theorem

Radouan DAHER, Takeshi KAWAZOE, Hatem MEJJAOLI

著者情報

キーワード: Hardy’s theorem, Miyachi’s theorem, Radon transform, Dunkl transform, Chébli-Trimèche transform

ジャーナルフリー

2009 年 61 巻 2 号 p. 551-558

DOI https://doi.org/10.2969/jmsj/06120551

詳細

抄録

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 R^d and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.