Geodesic
A criterion for straightening a~Lipschitz surface in the Lizorkin--Triebel sense.~III
Matematičeskie trudy, Tome 13 (2010) no. 2, pp. 139-178

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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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     author = {A. I. Parfenov},
     title = {A criterion for straightening {a~Lipschitz} surface in the {Lizorkin--Triebel} {sense.~III}},
     journal = {Matemati\v{c}eskie trudy},
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     language = {ru},
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A. I. Parfenov. A criterion for straightening a~Lipschitz surface in the Lizorkin--Triebel sense.~III. Matematičeskie trudy, Tome 13 (2010) no. 2, pp. 139-178. http://geodesic.mathdoc.fr/item/MT_2010_13_2_a5/