We consider a class of hypoelliptic ultraparabolic operators in the form
under the assumption that the vector fields and are invariant with respect to a suitable homogeneous Lie group . We show that if are two solutions of on and , then each of the following conditions: can be bounded by , or both and are non negative, implies . We use a technique which relies on a pointwise estimate of the fundamental solution of .
Cite this article
Chiara Cinti, Uniqueness in the Cauchy problem for a class of hypoelliptic ultraparabolic operators. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 2, pp. 145–158DOI 10.4171/RLM/538