boundedness of littlewood-paley operators on heisenberg group

《boundedness of littlewood-paley operators on heisenberg group》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、第31卷第2期新疆大学学报(自然科学版)Vol.31,No.22014年5月JournalofXinjiangUniversity(NaturalScienceEdition)May,2014BoundednessofLittlewood-PaleyOperatorsonHeisenbergGroupZHOUJiang,LIPeng(CollegeofMathematicsandSystemSciences,XinjiangUniversity,Urumqi,Xinjiang830046,China)Abstract:Inthispaper,theboundedn

2、essofgeneralizedLittlewood-PaleyoperatorsgfromspaceHK˙;p(Hn)tospace;qK˙;p(Hn)isprovedwhereQ(11=q)6

3、,HeisenberggroupCLCnumber：O174.2DocumentCode：AArticleID：1000-2839(2014)02-0149-06Heisenberg群上Lilltewood-Paley算子的有界性周疆,李朋(新疆大学数学与系统科学学院，新疆乌鲁木齐830046)摘要：得到了Heisenberg群上的广义Littlewood-Paley算子g从HK˙;p(Hn)空间到K˙;p(Hn)空间的有界性,其中;qqQ(11=q)6

4、p(Hn)空间的有界性.;qq关键词：Littlewood-Paley算子,Herz型空间,Heisenberg群0IntroductionandMainResultTheLittlewood-Paleytheoryoriginatedinthe1930sanddevelopedinthelate1950s,isaveryeectivereplace-ment.Ithasplayedaveryimportantroleinharmonicanalysis,complexanalysisandPDE.TheLittlewood-Paley[1]gfunctionin

5、onedimensionwasfrstintroducedbyLittlewoodandPaleyinstudyingthedyadicdecompositionofFourierseries.AndthistheoryinhighdimensionwasestablishedbySteinin[2].ThebounedednessofLittlewood-pn[4]PaleyoperatorsgonL(R)wasobtainedbySteinin[3].LiandYangestablishedthehomogeneousHerzspacenestimatesfo

6、rLittlewood-Paleyoperatorsg,S;a,g;onR:kfkK˙;pn)6C1kg(f)kK˙;pn)6C2kS;a(f)kK˙;pn)6C3kg;(f)kK˙;pn)6C4kfkK˙;pn):q(Rq(Rq(Rq(Rq(RInthelastseveralyears,considerableattentionhasbeenpaidtothebehavioronHeisenberggroupHn.LiuandMa[5]establishedthebounedednessofLittlewood-PaleyoperatorsgonL

7、p(Hn).LiuandLu[6]establishedthebounedednessofLittlewood-PaleyoperatorsS,gonLp(Hn),andtheyalsogivedthehomogeneousHerzspaceestimatesforLittlewood-Paleyoperatorsg,S,;a;;agonHeisenberggroup:;kfkK˙;pn)6C1kg(f)kK˙;pn)6C2kS;a(f)kK˙;pn)6C3kg;(f)kK˙;pn)6C4kfkK˙;pn):q(Hq(Hq(Hq(Hq(HT