Intrinsic fractional Taylor formula

Abstract

We consider a class of non-local ultraparabolic Kolmogorov operators and a suitable fractional Holder spaces that take into account the intrinsic sub-riemannian geometry induced by the operators. We prove an intrinsic fractional Taylor formula in such spaces with global bounds for the remainder given in terms of the norm naturally associated to the differential operator.

Keywords

• non-local kolmogorov operator
• hypoelliptic operator
• hormander's condition
• intrinsic taylor formula