資源描述:
《球上加權(quán)bergman空間上的緊hankel算子new》由會員上傳分享,免費(fèi)在線閱讀,更多相關(guān)內(nèi)容在教育資源-天天文庫。
1、維普資訊http://www.cqvip.com南京大學(xué)學(xué)報(bào)數(shù)學(xué)半年刊第l7卷第2期JOuRNALOFN.~.NJINGUNIVERSITYVD】.17,No.22000年l1月MATHEMATICALBIQUARTERLYNov.,2000COMPACTHANKELoPERAToRSoNWEIGHTEDBERGMANSPACESINTHEUNITBALL’LiuYongmh~(Dept.ofMath.,XuzhouNormalUniversity,221009,Xuzhou.PRC)Abstr
2、actInthispaperstudyisgivenonthecornpac切e5softheToeplitzandHankeloperatorontheweightedBerg'mansl~.ceA‘(j(>1)intheunitballofc-.Itisshownthatthecoil],pactne~0ftheToeplitzandHankeloperatorwithsymbolf∈L(jdoesDOtdependonthewelghtedBergmanspaceA()(☆>1Keywor
3、dswelghtedBergmanspace.Toeplitzoperator,Hankdoperator.compactoper8t。rAMS(1991)subjectdassifieations47B38.41A351IntrOductiOnLetBB={2∈:I2l1一1.VistheLebesguemeasureandf。iaanormallza
4、—ti0nCOnstantchosensuchthatV。(B)=L.TherealnumberBwil1befixedinthepaper.For=(,,?一)一=(wl,:一?一W)∈P.weshalldenotetheinnerproductof=,zby(=.:∑≈andthenormof2bylizII=v/.Thespace0{holomorphicfun~tions0ni-1Bwillbedenotedby(B).For>1.wewriteL‘(B):L(B.a(chǎn)V.),J4。(B)
5、=上,‘(B)nH(B)and,11/JIIfll?If(:)㈨()}一Weknowthat(L(B)一II·ii)isaBanachspaceandA(B)isaclosedsubspace。fL戶。(B).TheoperatorP‘onL(B)isgivenby·Recei~'ed:Oct“,1999;Revised:Jun:82006作者慧介:劉永民·男,1957年2月生,基礎(chǔ)數(shù)學(xué)專業(yè).副教援.三發(fā)喪SmallHankP】oDe。rsoweightcdbe。gmanspacesofboun
6、dedsymmetricdomain等文章.維普資訊http://www.cqvip.com第2期劉永民;球上加權(quán)l(xiāng):~rgman空間上的緊Hankel算子·205‘P“
7、,(坤)=l,()0)dl,(),f∈工‘(),Bwhere:(2)=1/(1一(2,))“,,∈B.ChoseB.Cin[i]showsthat:P?is8boundedprojectionofL(B)ontoA。(B)and尸,()一,("),P7():,(0),Vf∈A‘().Write4,l~一esssupff,()j
8、:∈B),L(丑)一{f:B—C:Il,8?9、showthat:letJ2≥1andletfbeanalyticonB.Ⅳ,‘iscorn.pactonI4(B)ifandonlyifIili月lI2?=0.When'z—l,口一0,XiaoJ.inr43.showsthat:letfEL(B)andpE[1,∞),thenisacompactoperatoronA(B)ifandonlyifj_m(,一)(,·)}f..=0.TheauthorinIs]showsthat:letfEL‘(B),ifsup{·f·一P(,·)II?..w∈