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

数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (3): 369-378.

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

朱理

School of Mathematics, Wuhan University, Wuhan 430072, China

出版日期:2002-07-15 发布日期:2002-07-15

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

ZHU Li

School of Mathematics, Wuhan University, Wuhan 430072, China

Online:2002-07-15 Published:2002-07-15

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

22E25

朱理. A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP[J]. 数学物理学报(英文版), 2002, 22(3): 369-378.

ZHU Li. A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP[J]. Acta mathematica scientia,Series B, 2002, 22(3): 369-378.

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

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

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