抛物型算子及其交换子的有界性

《抛物型算子及其交换子的有界性》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、分类号O174密级UDC510编号10736硕士学位论文抛物型算子及其交换子的有界性研究生姓名：周承蓉指导教师姓名、职称：陶双平教授专业名称：应用数学研究方向：调和分析二〇一三年五月BoundednessofParabolicOperatorandItsCommutatorsChengrongZhou西北师范大学研究生学位论文作者信息论文题目抛物型算子及其交换子的有界性姓名周承蓉学号2010210793专业名称应用数学答辩日期2013.05.24联系电话13669352624E_mailZcrzcr1986zhou@126.com

2、通信地址(邮编)：备注：8¹ÁÁÁiAbstractiiiXXXØØØ10.1ïĵ...........................10.2ïÄyG...........................10.3©(Sü.......................2111!1!o!o÷o÷Ø÷ØÆØÆÔÆÔ.Ô.Û.ÛÉÛÉÈÉÈ©È©©ff9f99ff3f3232Â2ÂÂMorreymmþmþþkk.k.5.5551.1Úó9Ì(......................51.2̽ny²....

3、.................9111!!2o!o÷o÷Ø÷ØÆØÆÔÆÔ.Ô.Û.ÛÉÛÉÈÉÈ©È©©ff9f9Ù9ÙÙff3f33Hardymmþmþþkk.k.5.55172.1Úó9Ì(......................172.2̽ny²......................18111!3!C!CþCþØþØØÆÆÔÆÔ.Ô..Littlewood-Paleyff9f9Ù9ÙÙfff5kk.k.5.55273.1Úó9Ì(.....................

4、273.2̽ny².....................28ëëë©©z©zz43ÖÖaÖa¬a¬Æ¬ÆÆÏÏmÏmumuuØةة©4951Á©©ǑnÙ,ÌïÄÆÔ.f9Ùf3Aa¼êmþk.5.1!/Ïuo÷ØÆÔ.ÛÉÈ©fZΩ(y)Tf(x)=p.v.f(x−y)dyRnρ(y)αpLk.5ؼêΩ÷vaLipschitz^,T32ÂMorreyqmþk.5(.Ǒéþã(A^,Ω÷vaL-Dini^,b(x)ǑBMO¼ê,·Ǒy²o÷ØÆÔ.ÛÉÈ©pfZΩ(x

5、−y)mm[b,T](f)(x)=p.v.[b(x)−b(y)]f(y)dyRnρ(x−y)α32ÂMorreymþ´k..1!

6、^Hardym¥f©)nر9ÆÔ.BMOmêǑx,©o÷ØÆÔ.ÛÉÈ©f9ÙfZΩ(x−y)[b,T](f)(x)=p.v.[b(x)−b(y)]f(y)dyRnρ(x−y)αppαα´lHmLmþk.,Ù¥,max{α+β,α+1}

7、^CþØÆÔ.Littlewood-PaleyfZ∞Z1/2Ω(x

8、,x−y)dt2gϕ(f)(x)=

9、f(y)dy

10、0ρ(x−y)≤tρ(x−y)α−1t3qL(1

11、DΩ(x,ξ)

12、≤C(β)ξx∈Rn,ξ′∈Sn−1,gϕ9ÙfZ∞Z1/2Ω(x,x−y)2dt[b,gϕ](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-gularoperatorswithroughkernelsZΩ(y)Tf(x)=p.v.f(x−y)dy,Rnρ(y)

16、αtheboundednessresultsofTisestablishedonthegeneralizedMorreyspaces,whereΩisafunctionofhomogeneousofdegreezerowhichsatisfiesac