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

Published:2010-08-03
Printed: Mar 2011
• Yongyang Jin,
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China
• Genkai Zhang,
Department of Mathematics, Chalmers University of Technology and Göteborg University, Göteborg, Sweden
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## Abstract

We prove that the fundamental solutions of Kohn sub-Laplacians $\Delta + i\alpha \partial_t$ 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.
 MSC Classifications: 22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX] 35R03 - Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc. 43A80 - Analysis on other specific Lie groups [See also 22Exx]