非雙倍測度下一些算子的有界性.pdf

1、碗士研究生鬟經(jīng)論宓霸疆大學(xué)論褒題黔(聾文)：茹雙倍測度下一些算子的有界性鑣文題目灝文)蒜警囂篙m曬e80as“ur哪es叫驢糯幻瑙。n疆瓣日D鼙Dnn2研究生姓名：李蟄罐‘學(xué)科、專業(yè)；基礎(chǔ)數(shù)學(xué)7研究；一方向：調(diào)和分析導(dǎo)師姓名職稱：。江寅生教授。論文答辯日期2006年月‘B學(xué)位授予固期；一2006年月BprefaceDref&ceIt、swellknownthatthedoublingmeasuresplaysaimportantrole

2、inHar—monicAnMysis，Recently，peoplehavefoundainoremildconditiongrowthcon—dition，Letd，nbesomefixedintegerswith1≤％SdAssumingthat肚isaRadonmeasureonR“sarisfyingthefollowinggrowthcondition：“(B【z，r))≤Gr“x∈R4Ir0，B(x，r)=可∈Rd：I掣～。

3、【1)ifitisboundedi11工2f“1ThepaperwillextendtheresultsonHerzspaces，inparticular，weobtaintheweightedinequlitiesforvector—valuedCZO。11三之1。(R。)space，where—n盧n(q一1)Inchapteithree，hi2001Garcia—CuervaandMartell19provedthebound—e

4、dnessoffractionslintegraloperatorsfrom妒toLqwithnondoublingmeasuresIn2004SA、VANOandTANAKAfl0]obtainedtheboundednessofvector。valuedfractionalintegraloperatorsfron]I，toLowithllondoublingmeasuresThispaperwillextendthebounded

5、nessintoHerzspaceswithnon—doublingmeasures，wegivetheestimateforfractionalintegraloperatorsandi拓vector—valuedextensions，speci出堍(ql，92)estimateforpowerweightedfractionalinte—graloperatotsKeywords：commutators；CalderdnZygrnu