Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (3): 369-378.

• Articles • Previous Articles     Next Articles

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

 ZHU Li   

  1. School of Mathematics, Wuhan University, Wuhan 430072, China
  • Online:2002-07-15 Published:2002-07-15

Abstract:

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.

Key words: Laplace operator, fundamental solution, singular integral kernels, analysis on nilponent groups, regularity of solutions

CLC Number: 

  • 22E25
Trendmd