A regularity lemma for functions of several variables. (English) Zbl 0699.58008

The following theorem is proved: Let \(F_ s\) and \(F_ u\) be two continuous transverse foliations with uniformly smooth leaves. If f is uniformly smooth along the leaves of \(F_ s\) and \(F_ u\), then f is smooth. The theorem is a generalization of similar assertions on stable and unstable foliations of an Asonov diffeomorphism to the case of non- absolutely continuous foliations. Some special cases are mentioned, too.
Reviewer: J.Durdil


58C25 Differentiable maps on manifolds
57R35 Differentiable mappings in differential topology
Full Text: DOI EuDML