Improving the regularity of vector fields

摘要

Let alpha > 0, beta > alpha, and let X-1, ... , X-q be Wlo alpha c vector fields on a W alpha+1 manifold which span the tangent space at every point, where W-s denotes the Zygmund-Holder space of order s. We give necessary and sufficient conditions for when there is a W beta +1 structure on the manifold, compatible with its W alpha+1 structure, with respect to which X-1, ... , X-q are W-loc(beta). This strengthens previous results of the first author which dealt with the setting alpha > 1, beta > max{alpha, 2}. (C) 2022 Elsevier Inc. All rights reserved.