支撑在(-1%2c1)上的Carleson测度与相关的Hankel矩阵

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1、汕头大学硕士学位论文支撑在(-1,1)上的Carleson测度与相关的Hankel矩阵姓名：鲍官龙申请学位级别：硕士专业：基础数学指导教师：乌兰哈斯2010-04_V,k>n'!(−1,1)i(Carleson0~9(Hankel"µi[kDeBfBorel8sui>i(−1,1),#n&~1µip-Carleson8s(p>0)FeHankeldeke{x22℄µei>i(0,1)D(−1,0)&q?eHankeld:`eH1µip-Carleson8s(p≥1)e9^&q&~12Hilb

2、ertXDirichleteBpn℄-5}3h2℄r12.<:1Carleson8sX.<F#>&~ye?5Hankeldej(2H1#ne-m>h{℄&~1p-Carleson8sFeHankeldke{H-h1#ne-m>^&q?)?1#ne-m>/Xeh℄(?h{℄4Bem>&~12HilbertXDirichleteBpa%14Bem)9F'Carleson8sHankeldDirichletHilbertI_V,k>nCarlesonme

3、asuressupportedon(−1,1)andtherelatedHankelmatricesAbstractLetµbeafinitepositiveBorelmeasureonDsupportedon(−1,1),p>0.Westudytherelationshipbetweenp-CarlesonmeasureµandtheelementsoftherelatedHankelmatrix.Moreover,whenµissupportedon(−1,0)or(0,1),p≥1,wecharacterizep-Carlesonmeas

4、ureµintermsoftheoperatorsinducedbytherelatedHankelmatrix.Thethesisconsistsofthefollowingthreeparts.Thefirstpartisconcernedingivingthebackgroudsofsomefunctionspaces.TheimportanceofCarlesonmeasureinfunctonspacesandoperatortheoryisrecited;theknowledgeoftheHankelmatrixandthemain

5、resultesofthisthesisarealsolisted.Inthesecondpart,westudytherelationshipbetweenp-Carlesonmea-suresandtherelatedHankelmatrices.Wegiveandprovethemainresultesofthethesis.Atthesametime,weexplainthatthemainresultesarebestbyexamples.Finally,westudythegeneralizedHilbertoperatorson

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