On characterization of Poisson integrals of Schrodinger operators with BMO traces

الأصل · EN

Let L be a Schrodinger operator of the form L=-Δ+V acting on L²(Rn) where the nonnegative potential V belongs to the reverse Holder class Bq for some q>= n. Let BMOₗ(Rn) denote the BMO space on Rn associated to the Schrodinger operator L. In this article we will show that a function f in BMOₗ(Rn) is the trace of the solution of L'u=-uₜt+Lu=0, u(x,0)= f(x), where u satisfies a Carleson condition. Conversely, this Carleson condition characterizes all the L-harmonic functions whose traces belong to the space BMOₗ(Rn). This result extends the analogous characterization founded by Fabes, Johnson and Neri for the classical BMO space of John and Nirenberg.