非齊型空間上算子有界性的一些研究.pdf

1、首都師范大學(xué)碩士學(xué)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(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)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(cái)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