Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (4): 1583-1590.doi: 10.1016/S0252-9602(11)60344-5

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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).

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

CLC Number: 

  • 22E25
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