Characterization of temperatures associated to Schrödinger operators with initial data in BMO spaces

Let L be a Schrödinger operator of the form = − Δ + V acting on 2 ( R n ) where nonnegative potential belongs to reverse Hölder class B q for some ≥ . BMO denote space associated L. In this article we will show that function f ∈ is trace solution u : t 0 , x satisfies Carleson-type condition sup r ∫ | ∂ ∇ d ≤ C < ∞ Conversely, characterizes all L-carolic functions whose traces belong