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arXiv · 1707.01422

Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups

Stefano Pagliarani·Michele Pignotti
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Abstract

We prove an intrinsic Taylor-like formula for a class of Lie groups arising in the study of some sub-elliptic differential operators, namely the Kolmogorov operators. The estimate of the remainder is in terms of the intrinsic norm induced by such operators. These results extend the recent developments in a work by Pascucci and the present authors, where a full characterization of the intrinsic H\"older spaces and their Taylor polynomials were given under the additional assumption that the Lie group is homogeneous in the sense of Folland & Stein. Remarkably, the intrinsic Taylor polynomial admits the same representation as in the homogeneous case.

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Stefano Pagliarani, Michele Pignotti. 2017-07-05. Intrinsic Taylor formula for non-homogeneous Kolmogorov-type Lie groups. https://arxiv.org/abs/1707.01422

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