The classical Hardy theorem on $\rr$ was generalized by Miyachi and Bonami, Demange, and Jaming. In this paper we show that Miyachi's theorem and Bonami-Demange-Jaming's one can be reformulated for the Jacobi transform in terms of the heat kernel.
@article{1171377076,
author = {Daher, R. and Kawazoe, T.},
title = {Generalized Hardy's theorem for the Jacobi transform},
journal = {Hiroshima Math. J.},
volume = {36},
number = {1},
year = {2006},
pages = { 331-337},
language = {en},
url = {http://dml.mathdoc.fr/item/1171377076}
}
Daher, R.; Kawazoe, T. Generalized Hardy's theorem for the Jacobi transform. Hiroshima Math. J., Tome 36 (2006) no. 1, pp. 331-337. http://gdmltest.u-ga.fr/item/1171377076/