单位球上BMOA空间和Bloch型空间上的加权复合算子

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1、THEWEIGHTEDCOMPOSITION0PERATORONBMOAANDBLOCHTypeSPACEINTHEUNITBALLABSTRACTThedissertationcollectsthemainresultsobtainedbytheauthorMaster’8Degree．ThisstudymainlyconcernstheweightedcompositeoperatoronBMOAspaceandBloch-typespaceinn-dimensionunitballanddiscussestheb

2、ounded-nes8．compactnessandtheessentialnormoftheweightedcompositionoperator．ThefirstchaptergivestheresearchbackgroundofBMOAspace，Bloch-typespaceintheunitballandtheweightedcompositeoperator．Thenitgivessomenotations，conceptionsandtheoremsthatarenecessaryinthethesis

3、．Atthesametime，itintroducesthesignificanceofthisresearch．ThesecondchapterstudiestheweightedcompositeoperatorfromBMOAspacetoBloch—typespaceintheunitball．FortheresearchoftheweightedcompositionoperatorfromBMOAspacetoBlochspace，LiSongxiaohasgiventhesufficientandnece

4、ssaryconditionfortheweightedcompositionoperatortobeboundedintheunitdiscinthereference【1】．S．OhnohasgiventhesufficientandnecessaryconditionfortheweightedcompositionoperatorinBlochspaceandinthelittleBlochspacetobeboundedandcompactintheunitdiscinthereference【2】．Inth

5、ischapter，theresultscollectedfromaboveareusedintheunitballandInthethirdchapter，theauthorstudiestheweightedcompositeoperatorfromBMOAspacetolittleBloch-typespaceintheunitball．Thischapteristhegener-alizationoftheresultsinthereference【3】'discussingthesufficientandne

6、cessaryconditionfortheweightedcompositeoperatortobeboundedorcompactintheIIABSTRACTunitball．ThefourthchapterstudiestheessentialnormoftheweightedcompositionoperatorindifferentBloch·typespaceintheunitball，andgivestheupperboundandlowerboundoftheessentialnormofthewei

7、ghtedcompositionoperator．KEYWORDS：BlochSpace；Q—BlochSpace；卢-Blochspace；BMOAspace；weightedcompositionoperator；theboundednoss；；thecompactness；theessentialnormm目录摘要⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．．IABSTRACT⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯II同录⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯Ⅳ1绪论⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

8、⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．11．1历史概况⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯11．2一些记号与定义⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯31．3国内外研究现状⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯52单位球上从BMOA空间到Blo出型空间的加权复合算予⋯⋯⋯⋯⋯⋯⋯⋯．112．1一些引理⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯