關(guān)于Marcinkiewicz型算子及其交換子的某些估計.pdf

1、碩士研究生學(xué)位論文新疆大學(xué)論文題目(中文)：關(guān)于Marcinkiewicz型算子及其交換子的某些估計論文題目(外文)：SomeEstimatesforMarcinkiewiczTypeOperatorsaIldItsCc衄utators研究生姓名：趙發(fā)友學(xué)科、專業(yè)：基礎(chǔ)數(shù)學(xué)學(xué)位類別：理學(xué)碩士研究方向：調(diào)和分析及應(yīng)用導(dǎo)師姓名職稱：江寅生教授論文答辯日期2007年5月28日學(xué)位授予日期2007年月臼EnglishAbstractlIItis

2、weltknownthattheMarcinkiewiczintegraloperatorisveryimportantinharmonicanalysisMarcinkiewicz【1】consideredtheexpressionp(，)(z)givenby蘆∽∽=讎，刎墮業(yè)掣哆1／2艇捌，whereF(x)=屆捌f(t)dtIn1958，SteinintroducedthehigherdimensionMMarcinkiewics

3、integralsoperator№definedby刪=(f比Igf(xV)器咖㈣i／2加，∈如c阱Stein2】showedthatifgt∈已i孫(1弘一1)暖some0a≤1，thenl幻isaboundedoperatoronp(艫)for1P≤2，andaboundedmappingfromL1(艫)toweakL1(R“)In1990，TorchinskyandWangshiljn【13】introducedthedefi

4、nitionofthecommutatoroftheMarcinkiewiczintegralForb∈Lk(玨P)，thecommutatoroftheMarcinldewiczintegral‘幻jisdefinedas腳，b(，)(z)=(／I昂，ht(z)12age)，抵‰(z)=厶；。警器(6(壚咐))，(v)dvIf6($)∈BMO(R“)，they【13】showedthatifQ∈—L旬如(jsn一1)(o口≤1)，th

5、enfor1Po。，“∈如(theweightdassofMuckenhoupt’s)腳，6isboundedon妒∞)Inchapter1，theboundeduessontheweightedHerzspacesisestablishedfor8classofMarcinldewiczintegralcommutatorsgeneratedbyBMO(R“)functionsandMarcinkiewiczintegralswith

6、roughkernelsQ∈上，(p一1)，1r≤∞，andk一。Q(z)打(z)=0。Inchapter2，theboundednessonHerzspacesisestablishedforthehighordercommutatorsofMarcinkiewiczintegralgeneratedbyBMO(R“)functionswithQ∈L(109L)(m1)(伊一1)‘Inchapter3Westudythebounden

7、essofthecommutatorofMarcinkiewiczintegraloperatoronBMOP(R“)(BMOV(Ro)=BMO(R“)廠1L9(R“)(1P。。))Inchapter4，weshowthattheMarcinkiewiczoscillatoryintegralsisboundedon∥(R“)(2≤p(30)Furthermore，wealsogivetheendpointestimatefortheM