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

Minghua Yang and Chao Zhang

Mathematische Nachrichten, 2021, vol. 294, issue 10, 2021-2044

Abstract: Let L be a Schrödinger operator of the form L=−Δ+V acting on L2(Rn) where the nonnegative potential V belongs to the reverse Hölder class Bq for some q≥n. Let BMOL(Rn) denote the BMO space on Rn associated to the Schrödinger operator L. In this article we will show that a function f∈BMOL(Rn) is the trace of the solution of Lu:=ut+Lu=0,u(x,0)=f(x), where u satisfies a Carleson‐type condition supxB,rBrB−n∫0rB2∫B(xB,rB)t|∂tu(x,t)|2+|∇xu(x,t)|2dxdt≤C

Date: 2021
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