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. 
@article{MZM_2007_81_4_a1,
     author = {E. I. Berezhnoi},
     title = {On {Subspaces} of $C[0,1]$ {Consisting} of {Nonsmooth} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {490--495},
     publisher = {mathdoc},
     volume = {81},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_4_a1/}
}
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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/