A class of solvable non-homogeneous differential operators on the Heisenberg group

Detlef Müller¹ ; Zhenqiu Zhang²

¹ Mathematisches Seminar Christian-Albrechts-Universität Kiel Ludewig-Meyn-Str. 4 24098 Kiel, Germany
² Department of Mathematics Tianjin University 300072 Tianjin, P.R. China

Studia Mathematica, Tome 148 (2001) no. 1, pp. 87-96

Résumé

In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group ${\mathbb H}_n$, whose principal parts are “positive combinations of generalized and degenerate generalized sub-Laplacians”, and which are homogeneous under the Heisenberg dilations. In this note, we shall consider the same class of operators, but in the presence of left invariant lower order terms, and shall discuss local solvability for these operators in a complete way. Previously known methods to study such non-homogeneous operators, as in [9] or [6], do not apply to these operators, and it is the main purpose of this article to introduce a new method, which should be applicable also in much wider settings.

Détail

DOI : 10.4064/sm148-1-8

Keywords: studied problem local solvability complex coefficient second order left invariant differential operators heisenberg group mathbb whose principal parts positive combinations generalized degenerate generalized sub laplacians which homogeneous under heisenberg dilations note shall consider class operators presence invariant lower order terms shall discuss local solvability these operators complete previously known methods study non homogeneous operators apply these operators main purpose article introduce method which should applicable much wider settings