数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1583-1590.doi: 10.1016/S0252-9602(11)60344-5

• 论文 • 上一篇    下一篇

IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS

罗光洲   

  1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
  • 收稿日期:2008-11-27 修回日期:2009-12-18 出版日期:2011-07-20 发布日期:2011-07-20
  • 基金资助:

    This work was supported by National Science Foundation of China (10771175).

IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS

 LUO Guang-Zhou   

  1. School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
  • Received:2008-11-27 Revised:2009-12-18 Online:2011-07-20 Published:2011-07-20
  • Supported by:

    This work was supported by National Science Foundation of China (10771175).

摘要:

Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.

关键词: Heisenberg type group, heat kernel, Sobolev inequality, Galiardo-Nirenberg inequality

Abstract:

Motivated by the idea of M. Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds, we prove an analogous result for Kohn’s sub-Laplacian on the Heisenberg type groups. The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.

Key words: Heisenberg type group, heat kernel, Sobolev inequality, Galiardo-Nirenberg inequality

中图分类号: 

  • 22E25