Journé, Jean L. A regularity lemma for functions of several variables. (English) Zbl 0699.58008 Rev. Mat. Iberoam. 4, No. 2, 187-193 (1988). 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 Cited in 49 Documents MSC: 58C25 Differentiable maps on manifolds 57R35 Differentiable mappings in differential topology Keywords:differentiability; smooth functions of several variables; foliations PDFBibTeX XMLCite \textit{J. L. Journé}, Rev. Mat. Iberoam. 4, No. 2, 187--193 (1988; Zbl 0699.58008) Full Text: DOI EuDML