解析函数空间上的范数可取到算子.pdf

《解析函数空间上的范数可取到算子.pdf》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、?µúm)Û¼êmþêfNormAttainingOperatorsonAnalyticFunctionSpaces£öÞÆnÆa¬ÆØ©¤£X!¤¤µnÆêÆX;µÄ:êÆïÄ)µ4
²µ=¤UBÇOcoÆØ©M5(²Ø©´·<3e?1óïÄ9ïĤJ"Ø©¥ØAO±I5Ú/§Ø¹Ù¦<½Ù§Å®²uL½>LïĤJ"é©ïÄÑz<Ú8N§þ®3Ø©¥±²(ªI²"<¿£(²{ÆI?d<«ú"Ø©ö¶µFϵcFÆØ©¦^Ç(²<ÇöÞÆ

2、ÆØ©>fÚ©§#NØ©Ú/¶ÆòÆØ©ܽܩSN?k'êâ¥?1u¢§±æ^K

3、g∈H(D)ѱpÈ©fZz0Ig:f→f(w)g(w)dw.0©¥,·ÌïÄùüafê¯K.©Ù̹±enÜ©:1Ù,0üþ²;¼êm,)Hardym,Bergmanm,Blochm9DirichletmÄVg,PÒ9µ£;êf½Â9µ.1Ù,ïÄlBαBβEÜfC.·ÑCêOϕϕª,Cϕ´ê¿©7^.1nÙ,ïÄ3Blochm,Dirichletm9BMOAmþÈ©fIg.Igê,ÓÄIgê¯K.'''ccc:EÜf,È©f,ê,¼êm.IöÞÆa¬ÆØ©A

4、bstractLetDbetheunitdiscofcomplexplaneandϕbeaholomorphicmappingfromDtoitself.DenoteH(D)thespaceofallanalyticfunctionsonD.ThenϕinducesacompositionoperatorCϕ:f→f◦ϕ.Foranyg∈H(D),itcaninduceanintegraloperatorZz0Ig:f→f(w)g(w)dw.0Inthisthesis,Norm-attainingcompositionoper

5、atorsandNorm-attaininginte-graloperatorsareinvestigated.Therearethreepartsinthisthesisasfollowing.Thefirstchapterisconcernedindefinitionsandbackgroundsofsomeclas-sicalfunctionspacesandnorm-attainingoperators.Somerelativeresultsarealsolisted.Chapter2isaimedatinvestigat

6、ingthecompositionoperatorsfromBαtoBβ.ThenormofCisestimated.Wearealsogivenecessaryandsufficientϕconditionsfornorm-attainingcompositionoperatorCϕ.Inchapter3,westudytheintegraloperatorIgontheBlochspace,DirichletspaceandBMOAspace.Wegivesomeconditionsforintegraloperatorsto

7、benorm-attaining.Keywords:compositionoperator,integraloperator,norm-attaining,functionspace.IIIöÞÆa¬ÆØ©IVöÞÆa¬ÆØ©888¹¹¹¥¥¥©©©ÁÁÁ·································I===©©©ÁÁÁ·································III888¹¹¹································V1111ÙÙÙÚÚÚóóó·······

8、······················11.1uÐ{¤····························11.2ý£····························21.3©Ì(J························51112ÙÙÙ\