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1、維普資訊http://www.cqvip.com第29卷第3期湘潭大學(xué)自然科學(xué)學(xué)報VoI.29No.32007年9月NaturalScienceJournalofXiangtanUniversitySept.2007CompactProductsofHankelandToeplitzOperatorsonWeightedBergmanSpaceTANGShu—l∞曜(DepartmentofMathematics。XiangtanUniversity。Xiangtan411105China)【Abstract】In
2、thispaper。wesivcasuficientandnecessaryconditionthattheproductsofToeplitzandHankeloperators’。foranalyticfuncfionsf,giscompactontheweightedBergmanspace(D。(I+a)(I—I:I)dA(z)).Keywords:WeightedBergmanspace;ProductsofToeplltzandHankeloperators;Compactoperator加權(quán)Bergm
3、an空間上的緊Toeplitz和Hankel算子積唐樹江(湘潭大學(xué)數(shù)學(xué)系,湖南湘潭4l1105)【摘要】主要考察一類加權(quán)Bergman空間上的緊算子,得到了當(dāng)f,g是解析函數(shù)時,Tocplitz和Hankel算子的積7H.’是緊算子的充分必要條件.關(guān)鍵詞:加權(quán)Bergman空間;Toeplitz和Hankel算子積;緊算子中圈分類號:0177.1文獻(xiàn)標(biāo)識碼:A文章編號:1000—5900(2007)02—0029—081IntroductionLetdAdenotetheLebesgueareameasureont
4、heunitdiskDnormalizedSOthatthemeasureofDequalsto1.Andfor∈(一1,∞),letdA。denotethemeasuredA。(z)=(1+)(1-IzI)。da(z),forp∈[1,∞),LP(D,dA。)isaBanachspace.L”(D,dA)isthesetofessentiallyboundedfunctiononD,and(D,dA。)isaclosedsubspaceconsistingofanalyticfunctioninL”(D,dA。)
5、.Inthispaperwedenote(D,dA。)by(dA。).ThentheweightedBergmanspaceL:(dA。)isaHilbertspaceconsistingofanalyt—icfunctioninL(D,dA。),andwedenoteainnerproductonL(D,dA。)by=(JDu(z)t,(z)da。(z))蠆foreveryl‘,t,∈L(D,dA。).Fromconclusionof[1],weknownthat:(dA。)isareproduci
6、ngkernelHil—bertspaceonDwithreproducingkernel:1()‘rorf∈L2(D,dA。),Toeplitzoperator巧andHankeloperatorwithsymbolfaredefinedontheBerg-man(weighted)spaceL:(dA。)byIl=P。),Vh∈L:(dA)andIl=(1一P)),Vh∈L:(dA。)forallpolynomialsh,wherePaistheorthogonalprojectionfromL2(D,dA。)
7、to(dA。).DuetoreproducingpropositionsoftheweightedBergmanspaceweobtainsomepropositionofToeplitzand·收稿日期:2005—06—12~作者簡介:唐樹江(1977一),男,湖南永州人,講師.E—mail:jl2snaker@163.com~.■h維普資訊http://www.cqvip.comNaturalScienceJournalofXiangtanUniversityHankeloperators:(P/)()=<廠,
8、>=(z),()()=(())()=『DdL4(z),(H/h)()=(1一))()=(1dL4()一i)一f0r∈(dL4)andw∈D.Thenfuncti。ns,thusdefinedare,infact,allalyticfui仰·KatelStoethofandD.Zheng[2]haveobtainedcompletecharacterizafi