Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions

We consider the Weinstein type equation ${\mathcal{L}}_{\lambda }u=0$ on $(0,\mathrm{\infty })\times (0,\mathrm{\infty })$, where $$\mathcal{L}$_\lambda=\partial _t^2+\partial _x^2-\frac{\lambda (\lambda -1)}{x^2}$,with$\lambda >1$. In this paper we characterize the solutions of ${\mathcal{L}}_{\lambda }u=0$ on $(0,\mathrm{\infty })\times (0,\mathrm{\infty })$ representable by Bessel-Poisson integrals of BMO-functions as those ones satisfying certain Carleson properties.