加权Dirichlet空间之间的总体紧复合算子列  

Collectively compact composition operator sequences between weighted Dirichlet space

作　　者：江治杰 

机构地区：[1]四川理工大学数学系,自贡643000

出　　处：《四川大学学报（自然科学版）》2008年第6期1317-1322,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省教育厅重点项目(0720A04)

摘　　要：设φn:D→D为解析映射列,作者详细讨论了加权Dirichlet空间之间复合算子列{Cφn}的总体紧性,得到以下主要结论:(i)当Cφn:D2α→D2β(α,β>0)为一致有界复合算子列时,{Cφn}总体紧的充要条件;(ii)当Cφn:D2α→D2β(α,β≥1)一致有界复合算子列时,{Cφn}总体紧的充要条件.Let {ψn：D→D } be a sequence of analytic mappings and { Cψn：Dα^2→Dβ^2} be a sequence of compostion operators between different Dirichlet spaces. The author discusses the collective eompactess of such sequences, and the main results are obtained as follows： （i） The necessary and sufficient condition for the uni- form boundedness of the composition operator sequence { Cψn：Dα^2→Dβ^2（α,β〉0} ; （ii） the necessary and sufficient condition for the uniform boundedness of the composition operator sequence {Cψn：Dα^2→Dβ^2（α,β≥1}.

关 键 词：DIRICHLET空间 加权DIRICHLET空间 复合算子 总体紧算q-~ l 

分 类 号：O174.56[理学—数学]