Heat kernel and semigroup estimates for sublaplacians with drift on Lie groups (Q2574022)

The author obtains an estimate for the Davies perturbation of the semigroup generated by a centered sublaplacian \(H\) on a Lie group \(G.\) This result consists of a new form of \(L^2\) off-diagonal estimate for such semigroups. A new proof is given of the Gaussian heat kernel estimates established by \textit{N. T. Varopoulos} for amenable Lie groups [Can. J. Math. 55, No.~2, 401--431 (2003; Zbl 1042.58013)] and by \textit{G. K. Alexopoulos} for Lie groups of polynomial growth [Mem. Am. Math. Soc. 739, 101 p. (2002; Zbl 0994.22006); C. R. Acad. Sci., Paris, Sér. I, Math. 326, No.~5, 539--542 (1998; Zbl 0909.22019)].