On Characterization of Poisson Integrals of Schr?dinger Operators with Morrey Traces  

作　　者：Liang SONG Xiao Xiao TIAN Li Xin YAN 

机构地区：[1]Department of Mathematics, Sun Yat-sen University

出　　处：《Acta Mathematica Sinica,English Series》2018年第4期787-800,共14页数学学报（英文版）

基　　金：supported in part by Guangdong Natural Science Funds for Distinguished Young Scholar(Grant No.2016A030306040);NSF of Guangdong(Grant No.2014A030313417);NNSF of China(Grant Nos.11471338 and 11622113);the third author is supported by the NNSF of China(Grant Nos.11371378 and 11521101);Guangdong Special Support Program

摘　　要：Let L be a Schrodinger operator of the form L = -△ ＋ V acting on L2（Rn） where the nonnegative potential V belongs to the reverse Holder class Bq for some q _〉 n. In this article we will show that a function f∈ L2,λ（Rn）, 0 〈λ 〈 n, is the trace of the solution of Lu = -utt ＋ Lu = O, u（x, 0） = f（x）, where u satisfies a Carleson type condition sup t-λB xB,rB∫τB 0∫B（xB,τB）t{ u（x,t）}2dxdt≤C〈∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces .L2,λL（Rn） associated to the operator L, i.e. Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L2,λ（Rn） for all 0 〈λ〈 n.Let L be a Schrodinger operator of the form L = -△ ＋ V acting on L2（Rn） where the nonnegative potential V belongs to the reverse Holder class Bq for some q _〉 n. In this article we will show that a function f∈ L2,λ（Rn）, 0 〈λ 〈 n, is the trace of the solution of Lu = -utt ＋ Lu = O, u（x, 0） = f（x）, where u satisfies a Carleson type condition sup t-λB xB,rB∫τB 0∫B（xB,τB）t{ u（x,t）}2dxdt≤C〈∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces .L2,λL（Rn） associated to the operator L, i.e. Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L2,λ（Rn） for all 0 〈λ〈 n.

关 键 词：SchrSdinger operators Dirichlet problem Morrey spaces Campanato spaces Poissonsemigroup 

分 类 号：O177[理学—数学]