Approximation and Interpolation in Kolmogorov-type groups

TL;DR

This paper characterizes non-Euclidean H"older spaces associated with Kolmogorov-type operators using real interpolation, and establishes an approximation property for intrinsically regular functions in these spaces.

Contribution

It provides a novel real interpolation characterization for non-Euclidean H"older spaces linked to Kolmogorov operators, and proves an approximation property for regular functions.

Findings

Established a real interpolation characterization for non-Euclidean H"older spaces.

Proved an approximation property for intrinsically regular functions.

Linked the Lie structure of Kolmogorov operators to function space properties.

Abstract

We prove a real interpolation characterization for some non Euclidean H\"older spaces, built on the Lie structure induced by a class of ultra-parabolic Kolmogorov-type operators satisfying the H\"ormander condition. As a by-product we also obtain an approximation property for intrinsically regular functions on the whole space.