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1、南京師范大學博士學位論文單位球上的α-Bloch空間及其間的復合算子姓名:張敏珠申請學位級別:博士專業(yè):基礎數(shù)學指導教師:陳懷惠20070301摘要本文研究單位球上的n.Bloch空間之間的復合算子.乘積算子和日*到∞Bloch空間的加權復合算子.在本文中,首先引入新的度量口(口),給出了單位球上的a-Bloch函數(shù)的等價范數(shù),推廣TTimoney關于單位球上的Bloch函數(shù)的結果.同時也給出了單位球上的d、a-Bloch函數(shù)的等價刻劃.其次借助度量囂(口),我們完整地研究了單位球上a-Bloch空間之間的復合算子的有界性和緊性,得到了相應的充分必要條件
2、.同時還研究了單位球上日。到*B10ch空問的加權復合算子的有界性和緊性,也得到了相應的充分必要條件.改進了李頌孝和S.Stevid的相關結果.最后,我們完整地討論了單位球上a-Bloch空間之間的乘積算子的下有界性.得到了下有界性的充分必要條件.關鍵詞:a-Bloch空間,上P,復合算子,乘積算子,加權復合算子,有界性,緊性,下有界性.VAbstractInthisthesis,weinvestigatecompositionoperatorsandmultiplicationoperatorsbetweenn—Blochspaces,andweigh
3、tedcompositionoperatorsof日”inton—Blochspacesontheunitball.First,weintroduceanewmetric毋。("),andthen,theequivalentnorliisofa-Blochfunctionsontheunitballaregiyen,whichextendtheresultofTimoneyforBlochfunctionsontheunitball.Meanwhile,wegiveequivalentdefinitionsofthelittleoPBlochfuncti
4、onsontheUnitball.Second,byusingthemetricj}("),wecharacterizetheboundednessandcompactnessofcompositionoperatorsbetweena-BlochspacesontheunitballandobtainnecessaryandsufficientconditionsofboundedueasandcA)m-padne鵠.Wbals0establishne。e昭甜yandsu國cientconditionsofthebound-ednessandcompa
5、ctnessofweightedcompositionoperatorsofHOOinto∞Blochspacesontheunitball,whichimprovetheresultofS.X.LiandS.Stevid.Atlast,theboundednessfrombelowofmultiplicationoperatorsbetweena-Blochspacesoftheunitballisstudiedcompletely.Keywords:a-Blochspaces,日”,compositionoperator,multiplica-tio
6、noperator,weightedcompositionoperator,boundedness,compactness,boundedneesfrombelOW.PrefaceFunctionspaceshavebeenacentraltopicinmodernanalysis,andsomenewfunctionspacesarenowofincreasinguseinareassuchascomplex,Fourier,harmonicandfunctionalanalysis,andpartialdifferentialequationsand
7、theirapplications.Inadditiontotheclassical/2spaces,onehasamongothers,thedifferentiabilityscalesofSobolev,Besov,andLipschitzspaces,a8well∞BMOandVMO.Therearethefunctionspazesarisingincomplexanalysis,such嬲theBloch,DirichletandHardyspaces.Thestudyofcompositionoperatorsonanalyticfunct
8、ionspaceslinkssomeofthemostbasicquestion