Fundamental solution and sharp L-p estimates for Laplace operators in the contact complex of Heisenberg groups

被引：0

作者：

Baldi, Annalisa ^{[1
]}

Franchi, Bruno ^{[1
]}

Tesi, Maria Carla ^{[1
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

来源：

RICERCHE DI MATEMATICA | 2006年 / 55卷 / 01期

关键词：

Heisenberg groups; Differential forms; Currents; Laplace operators; Fundamental solution;

D O I：

10.1007/s11587-006-0009-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we construct a fundamental solution for the Laplace operator on the contact complex in Heisenberg groups H-n (Rumin's complex) relying on the notion of currents in H-n given recently by Franchi, Serapioni and Serra Cassano. This operator is of order 2 on k intrinsic forms for k not equal n, but is of order 4 on n intrinsic forms. As an application, we prove sharp L-p a priori estimates for horizontal derivatives.

引用

页码：119 / 144

页数：26