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Matematicheskie Zametki, 2007, Volume 81, Issue 4, Pages 490–495
DOI: https://doi.org/10.4213/mzm3692 (Mi mzm3692) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Subspaces of $C[0,1]$ Consisting of Nonsmooth Functions

E. I. Berezhnoi

P. G. Demidov Yaroslavl State University
Full-text PDF (430 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm3692
Abstract: 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, Lebesgue measure.
Received: 25.03.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 4, Pages 435–439
DOI: https://doi.org/10.1134/S0001434607030194
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: E. I. Berezhnoi, “On Subspaces of $C[0,1]$ Consisting of Nonsmooth Functions”, Mat. Zametki, 81:4 (2007), 490–495; Math. Notes, 81:4 (2007), 435–439
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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