Geodesic
HÖlder Spaces of Quasiconformal Mappings
Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 87

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Zbl
We prove that a $K$-quasiconformal mapping belongs to the little Hölder space $c^{0,1/K}$ if and only if its local modulus of continuity has an appropriate order of vanishing at every point. No such characterization is possible for Hölder spaces with exponent greater than $1/K$.
DOI : 10.2298/PIM0475087K
Classification : 30C62 26B35
Keywords: quasiconformal mappings, Hölder spaces, linear dilatation, modulus of continuity 
Leonid V. Kovalev. HÖlder Spaces of Quasiconformal Mappings. Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 87 . doi: 10.2298/PIM0475087K
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     title = {H\"Older {Spaces} of {Quasiconformal} {Mappings}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {87 },
     year = {2004},
     volume = {_N_S_75},
     number = {89},
     doi = {10.2298/PIM0475087K},
     zbl = {1086.30023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0475087K/}
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