Geodesic
On Subspaces of $C[0,1]$ Consisting of Nonsmooth Functions
Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 490-495.

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For each Hölder space $H^\omega$, we construct an infinite-dimensional closed subspace $G$ of $C[0,1]$, isomorphic to $l^1$ and such that, for each function $x\in G$ not identically zero, its restriction to the set of positive measure does not belong to the Hölder space $H^\omega$.
Keywords: Banach space, nonsmooth function, modulus of continuity
Mots-clés : Lebesgue measure. 
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E. I. Berezhnoi. On Subspaces of $C[0,1]$ Consisting of Nonsmooth Functions. Matematičeskie zametki, Tome 81 (2007) no. 4, pp. 490-495. http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a1/

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