On characterization of Poisson integrals of Schrödinger operators with BMO traces

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...

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Bibliographic Details
Published in:Journal of functional analysis 2014-02, Vol.266 (4), p.2053-2085
Main Authors: Duong, Xuan Thinh, Yan, Lixin, Zhang, Chao
Format: Article
Language:English
Subjects:
BMO space
Carleson measure
Dirichlet problem
Lipschitz space
Poisson integrals
Reverse Hölder inequality
Schrödinger operators
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Summary: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=−utt+Lu=0, u(x,0)=f(x), where u satisfies a Carleson conditionsupxB,rBrB−n∫0rB∫B(xB,rB)t|∇u(x,t)|2dxdt⩽C
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2013.09.008