On the relative fundamental solutions for a second order differential operator on the Heisenberg group
Volume 145 / 2001
Studia Mathematica 145 (2001), 143-164
MSC: Primary 43A80; Secondary 35A08.
DOI: 10.4064/sm145-2-4
Abstract
Let $H_{n}$ be the $(2n+1)$-dimensional Heisenberg group, let $p,q\geq 1$ be integers satisfying $p+q=n$, and let $$ L=\sum _{j=1}^{p}( X_{j}^{2}+Y_{j}^{2}) -\sum _{j=p+1}^{n}(X_{j}^{2}+Y_{j}^{2}) , $$ where $\{ X_{1},Y_{1},\dots, X_{n},Y_{n},T\} $ denotes the standard basis of the Lie algebra of $H_{n}$. We compute explicitly a relative fundamental solution for $L$.
