Let \begin{document}$ {\rm BMO}_{\Delta_{N}}(\mathbb{R}^{n}) $\end{document} denote a BMO space on \mathbb{R}^{n} associated to Neumann operator \mathcal{L}: = -\Delta_{N} . In this article we will show that function f\in is the trace of solution {\mathbb L}u u_{t}+ \mathcal{L} u 0, u(x, 0) f(x), where satisfies Carleson-type condition \begin{eqnarray*} \sup\limits_{x_B, r_B} r_B^{-n}\int_0^{r_...

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

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