拋物型算子及其交換子的有界性

《拋物型算子及其交換子的有界性》由會(huì)員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在行業(yè)資料-天天文庫。

1、分類號(hào)O174密級(jí)UDC510編號(hào)10736碩士學(xué)位論文拋物型算子及其交換子的有界性研究生姓名：周承蓉指導(dǎo)教師姓名、職稱：陶雙平教授專業(yè)名稱：應(yīng)用數(shù)學(xué)研究方向：調(diào)和分析二〇一三年五月BoundednessofParabolicOperatorandItsCommutatorsChengrongZhou西北師范大學(xué)研究生學(xué)位論文作者信息論文題目拋物型算子及其交換子的有界性姓名周承蓉學(xué)號(hào)2010210793專業(yè)名稱應(yīng)用數(shù)學(xué)答辯日期2013.05.24聯(lián)系電話13669352624E_mailZcrzcr1986zhou@126.com

2、通信地址(郵編)：備注：81áááiAbstractiiiXXX???10.1??μ...........................10.2??yG...........................10.3?(Sü.......................2111!1!o!o÷o÷?÷???????.?.?.?é?éèéè?è??ff9f99ff3f3232?2??Morreymmtmttkk.k.5.5551.1úó9ì(......................51.2ì?ny2....

3、.................9111!!2o!o÷o÷?÷???????.?.?.?é?éèéè?è??ff9f9ù9ùùff3f33Hardymmtmttkk.k.5.55172.1úó9ì(......................172.2ì?ny2......................18111!3!C!CtCt?t???????.?..Littlewood-Paleyff9f9ù9ùùfff5kk.k.5.55273.1úó9ì(.....................

4、273.2ì?ny2.....................28?????z?zz43??a?a?a???????m?mumuu??????4951á??ǒnù,ì????.f9ùf3Aa?êmtk.5.1!/?uo÷???.?éè?fZ?(y)Tf(x)=p.v.f(x?y)dyRnρ(y)αpLk.5??ê?÷vaLipschitz^,T32?Morreyqmtk.5(.ǒét?(A^,?÷vaL-Dini^,b(x)ǒBMO?ê,·ǒy2o÷???.?éè?pfZ?(x

5、?y)mm[b,T](f)(x)=p.v.[b(x)?b(y)]f(y)dyRnρ(x?y)α32?Morreymt′k..1!

6、^Hardym￥f?)n?±9??.BMOmêǒx,?o÷???.?éè?f9ùfZ?(x?y)[b,T](f)(x)=p.v.[b(x)?b(y)]f(y)dyRnρ(x?y)αppαα′lHmLmtk.,ù￥,max{α+β,α+1}

7、^Ct???.Littlewood-PaleyfZ∞Z1/2?(x

8、,x?y)dt2g?(f)(x)=

9、f(y)dy

10、0ρ(x?y)≤tρ(x?y)α?1t3qL(1

11、D?(x,ξ)

12、≤C(β)ξx∈Rn,ξ′∈Sn?1,g?9ùfZ∞Z1/2?(x,x?y)2dt[b,g?](f)(x)=

13、(b(x)?b(y))f(y)dy

14、0ρ(x?y)≤tρ(x?y)α?1t3ipp2α

15、reofthisthesis,whichconsistsofthreechapters,mainlystudythebound-ednesspropertiesoftheparabolicoperatorsandtheircommutatorsonsomefunctionspaces.Inthechapter1,byusingtheLpboundednesspropertiesoftheparabolicsin-gularoperatorswithroughkernelsZ?(y)Tf(x)=p.v.f(x?y)dy,Rnρ(y)

16、αtheboundednessresultsofTisestablishedonthegeneralizedMorreyspaces,where?isafunctionofhomogeneousofdegreezerowhichsatis?esac