1、首都師范大學碩士學位論文非齊型空間上算子有界性的一些研究姓名：趙冰申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：諶穩(wěn)固2003.3.1菲齊鷲空筒上算手有界性靜一些胬究3AbstractIn1950’SCalder6nandZygmundestablishedthefirstgenerationofCalder6n—ZygmundoperatorsFromthenon，ithasdevelopedintoaverywideresearchfi

2、eldJusttoni—parigtheprototypicalbook”Singularintegralsanddifferentiabilitypropertiesoffunctions’whichSteinwrotein1970withhisbook”Harmonicanalysis：Real—Variablemethods，Orthogonality；andOscillatoryintegrals”publishedin1993

3、，wefindtheonlyunchangedmatteristhattheunderlyingmeasure弘satisfiesthedoublingpropertyiethereexistsaconstantsC0suchthatu(B(x，2r))0，wherexisametricspacewithaBorelmeasure肛XTolsaestablishedLittlewood—PaleytheoryandT1theoryonn

4、on—homogeneousspaceinf19jFNazanov，STeilandAVolbergobtainedTbtheoryonnon—homogeneousin181and冷1whichbuiltupthetheoryframeofnon—homogeneousButtherearemanydi幣cultproblemsstillunsolvedThemainoneistoestabishHardyspacetheoryand

5、weightednorminequalitiesonnon—homogeneousspacesThesolutiontotheseproblmeswillnotonlyenrichsingularintegraloperatortheoryandfunctionspacetheory，butalsopushontheresearchofpartialdifferentialequationsThispaperincludesthepre

6、liminaryresearchofsingularintegrMoperatorsandrelatedoperators，In1181，XTolsaintroducedRBMO(z)spaceandasuitableSharpmaximalfunctionenjoyingpropertiessimilartOonesoftheclassicalSharpfunction：ie，f∈RBMO(IH)聿凈財襻f∈Lo。(弘)Aboutco

7、in—mutatorslb，，】，b∈RBMO(#)，TisaC—zoperatorwithmeasure般Tolsaobtainedtheboundednesson妒(弘)tnthefirstchapter，weobtainedweightednorminequalityonthecommutatorsbyprovingavariantofSharpfunctionestimates；JOrobitgandCP6rezintroduc

8、ed由weightsfornondoubingmeasuresandprovedweightednorminequality醴C。ZsingularintegralsInthesecondchapter，weobtainedweightedinequalitiesoffract，ionalintegralanditsmaximalfunctionwithA#∞)weightsfornondoubingmeasure；ESawyerobt