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Abstract
We consider a finite system {X1,X2, . . . ,Xn} of complete vector fields acting on a smooth manifold M equipped with a smooth positive measure. We assume that the system satisfies Hörmander's condition and generates a finite dimensional Lie algebra of type (R). We investigate the sum of squares of the vector fields operator corresponding to this system which can be viewed as a generalisation of the notion of Grushin operators. In this setting we prove the Poincaré inequality and LiYau estimates for the corresponding heat kernel as well as the doubling condition for the optimal control metrics defined by the system. We discuss a surprisingly broad class of examples of the described setting.
Original language  English 

Pages (fromto)  114 
Number of pages  14 
Journal  Journal of Lie Theory 
Volume  31 
Issue number  1 
Publication status  Published  2021 
Keywords
 Lie groups
 degenerate elliptic operators
 Grushin operators
 heat kernels
 Riesz transform
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Harmonic analysis of rough oscillations
Sikora, A., Portal, P., Hassell, A., Guillarmou, C. & van Neerven, J.
30/05/16 → …
Project: Research