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

Minghua Yang, Chao Zhang

Published 2017-10-02Version 1

Let L be a Schr\"odinger operator of the form L=-\Delta+V acting on L^2(\mathbb R^n) where the nonnegative potential V belongs to the reverse H\"older class B_q for some q>= n. Let BMO denote the BMO space associated to the Schr\"odinger operator L. In this article we will %study endpoint solvability result for the equation Lu =0 in upper plane having boundary values with BMO data, and show that a function f in BMO_L is the trace of the solution of u_t+L u=0, u(x,0)= f(x), where u satisfies a Carleson-type condition. Conversely, this Carleson condition characterizes all the L-carolic functions whose traces belong to the space BMO_L. This result extends the analogous characterization founded by Fabes and Neri for the classical BMO space of John and Nirenberg.