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ID:34365956
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页数:7页
时间:2019-03-05
《球上加权bergman空间上的紧hankel算子new》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、维普资讯http://www.cqvip.com南京大学学报数学半年刊第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.aV.),J4。(B)
5、=上,‘(B)nH(B)and,11/JIIfll⋯If(:)㈨()}一Weknowthat(L(B)一II·ii)isaBanachspaceandA(B)isaclosedsubspace。fL户。(B).TheoperatorP‘onL(B)isgivenby·Recei~'ed:Oct“,1999;Revised:Jun:82006作者慧介:刘永民·男,1957年2月生,基础数学专业.副教援.三发丧SmallHankP】oDe。rsoweightcdbe。gmanspacesofboun
6、dedsymmetricdomain等文章.维普资讯http://www.cqvip.com第2期刘永民;球上加权l:~rgman空间上的紧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∈
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∈
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