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

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