The classical Hardy theorem on , which asserts and the Fourier transform of cannot both be very small, was generalized by Miyachi in terms of and -functions. In this paper we generalize Miyachi's theorem for and then for other generalized Fourier transforms such as the Chébli-Trimèche and the Dunkl transforms.
Radouan DAHER. Takeshi KAWAZOE. Hatem MEJJAOLI. "A generalization of Miyachi's theorem." J. Math. Soc. Japan 61 (2) 551 - 558, April, 2009. https://doi.org/10.2969/jmsj/06120551