We consider the Weinstein type equation Lλu=0 on
(0,∞)×(0,∞), where Lλ=∂t2+∂x2−x2λ(λ−1), with λ>1. In
this paper we characterize the solutions of Lλu=0 on
(0,∞)×(0,∞) representable by Bessel-Poisson integrals of
BMO-functions as those ones satisfying certain Carleson properties