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1、References[1]A.BonamiandJ.L.Clerc,SommesdeCes’aroetmultiplicatiursdesdéveloppementsenhar2monicssphériques,Trans.Amer.Math.Soc.,183(1973),223-263.[2]S.Helgason,DifferentialGeometryandSymmetricSpaces,AcademicPress,NewYork,1962.[3]LiLuoqing,ApproximationforsphericalfunctionsbyBo
2、chner2Rieszmeans,Approx.TheoryandItsAppl.,7(1991),93-120.[4]LiLuoqing,Onapproximationofcertainmultiplieroperatorsonsetsoftotalmeasure,SinicaActaMath.,36(1993),28-34.[5]E.M.Stein,LocalizationandsummabilityofmultipleFourierseries,ActaMath.,100(1958),93-147.[6]H.C.Wang,Two2point
3、homogeneousspaces,Ann.ofMath.,55(1952),177-191.紧对称空间上Riesz平均的强逼近杨 汝 月李 落 清(宁夏大学数学系,银川750021)(北京师范大学数学系,北京100875)陈 迪 荣(中国科学院数学研究所,北京100080)摘要本文在紧对称空间中给出了全测度集上Riesz平均强逼近的阶.—189—©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.JournalofMathematicalResearch&Expositi
4、onVol.17,No.2,185-189,May1997StrongApproximationbyRieszMeansonCompactXSymmetricSpacesYangRuyueLiLuoqing(NingxiaUniversity,Yinchuan750021)(BeijingNormalUniversity,Bejing100875)ChenDirong(Inst.ofMath.,AcademiaSinica,Beijing100080)AbstractTheratesofstrongapproximationbyRieszmean
5、soncompactsymmetricspacesareestab2lished.Keywordsstrongapproximation,Rieszmeans,symmetricspace.ClassificationAMS(1991)41A25öCCLO174.41pLetMbead2dimensional(d>1)compactRiemanniansymmetricspaceofrankone.ByL(M),1Fp<∞,wedenotethespaceof(theequivalenceclassesof)p2integrablefunctio
6、nsonMwiththenorm1öpp‖f‖p:=∫ûf(x)ûdm(x),MdmbeingtheinvariantnormalizedRiemannianmeasureonM.Weknowthatwiththeexceptionofthecirclethecompactsymmetricspacesofrankoneco2[6]incidewiththecompacttwo2pointhomogeneousspaces(see[2]p.355).H.C.WanghasdshownthatMisoneofthefollowingfivetype
7、s,thesphere2d,therealprojectivespaceP(R),ddthecomplexprojectivespaceP(C),thequaternionicprojectivespaceP(H),andtheCayleyel216lipticplaneP(Cay),whereddenotethedimensionofMasamanifoldoverthereals.Let$betheLaplace2BeltramioperatoronMandlet∞2L=ÝHnn=02bethedecompositionofthespaceL
8、inadirectorthogonalsumoffinitedimensionalsubspaces22Hn.ThesubspacesH
