Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

Journal article, 2011

We prove that the fundamental solutions of Kohn sub-Laplacians Delta+i alpha partial derivative(t) on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in alpha with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.