Intrinsic Taylor Formula for Non-homogeneous Kolmogorov-Type Lie Groups

In this note we prove an intrinsic Taylor-like formula for a class of Lie groups arising in the study of some Kolmogorov operators of degenerate-type. The estimate of the remainder is in terms of the intrinsic norm induced by such operators. These results naturally extend those in Pagliarani et al. (J Math Anal Appl 435:1054–1087, 2016), where a full characterization of the intrinsic Hölder spaces and their Taylor polynomials were given under the additional assumption that the Lie group is homogeneous in the sense of Folland and Stein (Hardy Spaces on Homogeneous Groups. Mathematical Notes, vol. 28. Princeton University Press, Princeton, 1982). The intrinsic Taylor polynomial admits the same representation as in the homogeneous case.