We study the local existence and regularity of the density of the law of a functional on the Wiener space which satisfies a criterion that generalizes the Hörmander condition of order one (i.e., involving the first-order Lie brackets) for diffusion processes.
"Regularity of Wiener functionals under a Hörmander type condition of order one." Ann. Probab. 45 (3) 1488 - 1511, May 2017. https://doi.org/10.1214/16-AOP1092