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Heisenberg型群上的几类Hardy型不等式 被引量:2

SEVERAL HARDY TYPE INEQUALITIES ON GROUPS OF HEISENBERG TYPE
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摘要 文章得到了Heisenberg型群上的几类Hardy型不等式,并确定出了次Laplace算子的Hardy型不等式中的最佳常数. In this paper, several Hardy type inequalities on groups of Heisenberg type are proved. The best constant in the Hardy type inequality for the sub-Laplacian is determined.
出处 《系统科学与数学》 CSCD 北大核心 2005年第5期588-598,共11页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(10371099)资助课题.
关键词 Heisenberg型群 HARDY型不等式 PICONE恒等式 最佳常数 LAPLACE算子 Group of Heisenberg type, Hardy type inequality, Picone's identity, best constant.
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参考文献8

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同被引文献10

  • 1原子霞,钮鹏程.H型群上p-次Laplace算子的Hopf型引理和强极大值原理[J].Journal of Mathematical Research and Exposition,2007,27(3):605-612. 被引量:2
  • 2KAPLAN K.Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms[J].Trans.Amer.Math.Soc.,1980,258(1):147-153.
  • 3GAROFALO N,VASSILEV D.Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type[J].Duke Math.J.,2001,106(3):411-448.
  • 4FEDERER H.Geometric Measure Theory[M].Springer-Verlag New York Inc.,New York 1969.
  • 5CAPOGNA L,DANIELLI D,GAROFALO N.Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations[J].Amer.J.Math.,1996,118(6):1153-1196.
  • 6HEINONEN J,HOLOPAINEN I.Quasiregular maps on Carnot groups[J].J.Geom.Anal.,1997,7(1):109-148.
  • 7GAVEAU B.Principe de moindre action,propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents[J].Acta Math.,1977,139(1-2):95-153.
  • 8GAROFALO N,LANCONELLI E.Frequency functions on the Heisenberg group,the uncertainty principle and unique continuation[J].Ann.Inst.Fourier (Grenoble),1990,40(2):313-356.
  • 9廖家锋,李红英,段誉.一类奇异p-Laplacian方程正解的唯一性[J].西南大学学报(自然科学版),2016,38(6):45-49. 被引量:6
  • 10王胜军,韩亚洲.Baouendi-Grushin p-退化椭圆算子的广义Picone恒等式及其应用[J].西南师范大学学报(自然科学版),2018,43(3):1-6. 被引量:3

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