Real Analysis Exchange

Infinite Dimensional Banach Space of Besicovitch Functions

Jozef Bobok

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Abstract

Let $C([0,1])$ be the set of all continuous functions mapping the unit interval $[0,1]$ into $\mathbb{R}$. A function $f\in C([0,1])$ is called Besicovitch if it has nowhere one-sided derivative (finite or infinite). We construct a set $\mathcal{B}_{\sup}\negthickspace\subset C([0,1])$ such that $(\mathcal{B}_{\sup},\vert\vert~\vert\vert_{\sup})$ is an infinite dimensional Banach (sub)space in C([0,1]) and each nonzero element of $\mathcal{B}_{\sup}$ is a Besicovitch function.

Article information

Source
Real Anal. Exchange, Volume 32, Number 2 (2006), 319-334.

Dates
First available in Project Euclid: 3 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1199377475

Mathematical Reviews number (MathSciNet)
MR2369847

Zentralblatt MATH identifier
1213.46024

Subjects
Primary: 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

Keywords
Besicovitch function infinite dimensional Banach spac

Citation

Bobok, Jozef. Infinite Dimensional Banach Space of Besicovitch Functions. Real Anal. Exchange 32 (2006), no. 2, 319--334. https://projecteuclid.org/euclid.rae/1199377475


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