We consider the Kolmogorov–Fokker–Planck operator
in unbounded domains of the form
Concerning and , we assume that is what we call an (unbounded) admissible -domain: satisfies a uniform Lipschitz condition, adapted to the dilation structure and the (non-Euclidean) Lie group underlying the operator , as well as an additional regularity condition formulated in terms of a Carleson measure. We prove that in admissible -domains the associated parabolic measure is absolutely continuous with respect to a surface measure and that the associated Radon–Nikodym derivative defines an weight with respect to this surface measure. Our result is sharp.
"The $A_\infty$-property of the Kolmogorov measure." Anal. PDE 10 (7) 1709 - 1756, 2017. https://doi.org/10.2140/apde.2017.10.1709