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BMO研究近况

引言 BMo函数空间是1961年John和Nirenberg[‘]提出的.2971年C.Fefferman[2〕发现了BMO空间的几个重耍性质(也可参见〔3〕).此后,对BMO的研究迅速活跃起来,各种BMO空I司相继出现,BMo技术被广泛应用.1980年,Carleson在第18次Seandinavia数学家大会_L对BMO的十年发展作了很好的总结[‘J.我国开展BMO的研究可以说从80年代开始,、经过数年努力一也已取得不少戍果。本文试图对近几年BMO的研究工作做一粗略的介绍。诚然,这不是一个全面的概括,它侧重于作者戚兴趣的课题。设f(x)任Llloe(R”)Q是R’BMO定义的自身改进中表面平行于坐标平面的方体(以下简称方体),若满足条件S·P渝J。,‘一“·o骨x羊夕,(e)存在常数K,使d(x,夕)镇K{d(x,:)+d(:,夕)}对一切x,夕,:任X成立。此外,存在常数。,使o。, 、、‘//1985年10月5日收到,1...  (本文共13页) 阅读全文>>

《数学季刊》2003年03期
数学季刊

Boundedness of Operators in Morrey Spaces over Vilenkin Groups

§ 1. IntroductionandtheResults  Inordertoinvestigatethelocallyregularityaboutthesolutionofthesecondorderellipticpartialdifferentialequations ,Morreyintroducedin[1 ]functionspacescalledMorreyspace,whichplaysanimportantroleinthereseachoflocallycharacteristicofthesolutionofpartialdifferentialequations[2 ,3,4 ] .So,itisnecessarytomakeclearsomeimportantoperator’sproper tiesinMorreyspace.Inthispaper ,wewillestablishbounded...  (本文共5页) 阅读全文>>

《Science China(Mathematics)》2018年07期
Science China(Mathematics)

The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation

1 IntroductionIn the recent decades,many people studied the elliptic equation=|w|2—2w十Aw in Q,y(1.1)u=0on4 then(1.1)has a nontrivial solution for all A0.In[13],for iV6 and A€(0,Ai),Cerami et al.proved the existence of sign-changing solutions.While for thecase is a ball,N^7 and A G(0,Ai),they also proved the existence of infinitely many radial solutionsto(1.1).There is a great deal of work on elliptic equations with c...  (本文共24页) 阅读全文>>

《福建师范大学学报(自然科学版)》2008年03期
福建师范大学学报(自然科学版)

一类Caffarelli-Kohn-Nirenberg型方程弱解的存在性

考虑如下Caffarelli-K ohn-N irenberg型椭圆方程的弱解的存在性:-d iv(u x 2a)-μu x 2(1+a)=λur-1 x a+up-1 x bp,x∈Ω\{0},u0,x∈Ω\{0},u=0,x∈Ω.(1)其中0∈Ω为RN(N≥3)中的具有光滑边界的有界开区域,λ0,a≤b0,使得对任意λ∈(0,Λ*),方程(1)至少存在两个弱解.1预备知识为叙述方便,定义X-1表示Banach空间X的对偶空间.Lq(,Ωx-γ)表示加权的Lq(Ω),其范数为u q,γ=(∫Ωx-γuqdx)1/q,定义对偶对〈u,v〉E-1,E=(∫x-2a u v-μx-2(1+a)uv)dx.定义1[6]c∈R,X是一个Banach空间,且I∈C1(X,R),I满足(PS)c条件,若对于X中任意满足I(un)c且‖I′(un)‖X-10的序列{un}都包含收敛子列.若对于任意的c∈R,(PS)c条件都满足,则I满足(PS...  (本文共4页) 阅读全文>>

《Analysis in Theory and Applications》2014年04期
Analysis in Theory and Applications

Some Characterizations of VMO(R~n)

1 IntroductionSuppose that f is a locally integrable function on Rnand Q?R nis a cube with sidesparalleling to coordinate axis.Denote by fQthe mean of f on Q,that is,fQ=1|Q|Qf(x)dx.For a0,letMa(f)=sup|Q|≤a1|Q|Q|f(x)-fQ|dx.A locally integral function f is said to belong to B MO(Rn)if there exists a constant C0such that supa0Ma(f)≤C.The minimal constant C is defined to be the B MO(Rn)normof f and denoted by f*.In 1975,...  (本文共12页) 阅读全文>>

《数学季刊》2002年03期
数学季刊

非紧集合上的Brezis-Nirenberg定理(英文)

InthemountainpassandsaddlepointtheoremoneisconceernedwithaC1functionalfonaBanachspaceE .Onewishestofindasolutionof f′(x) =θoratleastasequence{xn} E ,suchthatf(xn)c,f′(xn)θ ,forsomec∈R .Ageneralprocedurewasfor mulatedinBrezis_Nirenberg [1 ]asfollows.LetMbeametricspaceandletM beanonemptyclosedsubset≠M .DefineΓ ={p ∈C(M ,E) |p|M =p };(Where p isafixedcontinuousmaponM .)c=Infp∈ΓSupx∈Mf( p(x) ) ;c1=Supx∈M f( p (x)...  (本文共4页) 阅读全文>>