Commuting Dual Toeplitz Operators on the Harmonic Dirichlet Space  

作　　者：Jing Yu YANG Yin Yin HU Yu Feng LU Tao YU 

机构地区：[1]School of Mathematical Statistics, Chifeng University, Chifeng 024000, P. R. China [2]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2016年第9期1099-1105,共7页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11271059,11271332,11431011,11301047);NSF of Zhejiang Province(Grant Nos.LY14A010013,LY14A010021);Higher School Foundation of Inner Mongolia of China(Grant No.NJZY13298)

摘　　要：In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.

关 键 词：Dual Toeplitz operator harmonic Dirichlet space COMMUTATIVITY 

分 类 号：O177[理学—数学]