A criterion for straightening a~Lipschitz surface in the Lizorkin--Triebel sense.~III

A. I. Parfenov

Matematičeskie trudy, Tome 13 (2010) no. 2, pp. 139-178.

Résumé

We obtain two new equivalent quasinorms for unweighted isotropic Besov and Lizorkin–Triebel spaces in the epigraph of a Lipschitz function. The question on the straightening is studied, i. e., the question on the existence of a diffeomorphism taking the epigraph into a halfspace which preserves the Lizorkin–Triebel spaces of the same indices. A criterion for the straightening is established in terms of dyadic weighted inequality where oscillations of a given function on stretched dyadic cubes are involved.

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