广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (1): 29-34.

• • 上一篇    下一篇

Greiner算子在R2n+1上的Poincaré不等式及Hardy-Sobolev不等式

王胜军1, 窦井波2   

  1. 1.青海师范大学数学与信息科学系,青海西宁810008;
    2.西安财经学院统计学院,陕西西安710100
  • 收稿日期:2011-11-14 出版日期:2012-01-20 发布日期:2018-12-03
  • 通讯作者: 王胜军(1968—),男,河南温县人,青海师范大学副教授。E-mail:sjwang68@sina.com
  • 基金资助:
    国家自然科学基金资助项目(11101319);浙江省自然科学基金资助项目(Y6110118);陕西省教育基金资助项目(2010JK549)

Poincaré Inequality and Hardy-Sobolev Inequality for GreinerOperator in R2n+1

WANG Sheng-jun1, DOU Jing-bo2   

  1. 1.Department of Mathematics and Information Sciences,QinghaiNormal University,Xining Qinghai 810008,China;
    2.School of Statistics,Xi'an Institute of Finance and Economics,Xi'an Shaanxi 710100,China
  • Received:2011-11-14 Online:2012-01-20 Published:2018-12-03

摘要： 基于Greiner算子,建立函数的表示公式,获得了R2n+1上的一类Poincaré不等式,并利用已有的结果,得到R2n+1上的一类Hardy-Sobolev不等式,包含了已有文献的相关结果。

关键词: Greiner算子, 表示公式, Poincaré不等式, Hardy Sobolev不等式

Abstract: For the Greiner operator,Poincaré inequality in R2n+1 is established by using a representation formula.Then,Hardy-Sobolev inequality in R2n+1 is presented,which contains the existed results.

Key words: Greiner operator, representation formula, Poincaré inequality, Hardy-Sobolev inequality

中图分类号: 

  • O152.5
[1] GAROFALO N,SHEN Zhong-wei.Absence of positive eigenvalues for aclass of subelliptic operatrs[J].Math Ann,1996,304(1):701-715.
[2] 王胜军,窦井波.一类退化椭圆算子的强Hardy型不等式及其应用[J].广西师范大学学报:自然科学版,2010,28(1):18-22.
[3] 韩亚洲,金永阳,张书陶.各向异性Heisenberg群上一类Hardy-Sobolev型不等式[J].高校应用数学学报:A辑,2010,25(4):440-446.
[4] FRANCHI B,LU Guo-zhen,WHEEDEN R L.Representation formulas and weighted Poincaré inequalities for Ho¨rm-ander vector fields[J].Ann Inst Fourier Grenoble,1995,45(2):577-604.
[5] LU Guo-zhen.Weighted Poincaré and Soblev inequalities for vector fields satisfying Ho¨rmander's condition and applications[J].Revista Mat Iberoamericana,1992,8(3):367-439.
[6] LU Guo-zhen.The sharp Poincaré inequalities for free vector fields:an end point result[J].Revista Mat Iberoamericana,1994,10(2):453-466.
[7] CAPOGNA L,DANIELLI D,GAROFALO N.An embedding theorem and the Harnack inequality for nonlinear subelliptic equations[J].Commun PartialDiff Eqns,1993,18(9/10):1765-1794.
[8] ZHANG Hui-qing,NIU Peng-cheng.Hardy-type inequalities and Pohozaev-type identities for a class of p-degenerate subelliptic operators andapplications[J].Nonlinear Anal,2003,54(1):165-186.
[9] KOMBE I.On the nonexistence of positive solutions to nonlinear degenerate parabolic equations with singular coefficients[J].Applicable Analysic,2006,85(5):467-478.
[10] FOLLAND G,STEIN E.Hardy spaces on homogeneous groups[M].Princeton,NJ:Princeton University Press,1982:257-326.
[11] COHN W S,LU Guo-zhen.Best constants for Moser-Trudinger inequalities on the Heisenberg group[J].Indiana University Mathematics Journal,2001,50(4):1567-1591.
[12] BARBATIS G,FILIPPAS S,TERTIKAS A.A unified approach to improvedLp Hardy inequalities with best constants[J].Trans Amer Math Soc,2004,356(6):2169-2196.
No related articles found!
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发