Acta Mathematica Hungarica
Volume/Issue:
Volume 127: Issue 1-2
On vector-valued curves that allow a C1,α parametrization
Authors:
J. Duda PIRA Energy Group 3 Park Avenue, 26th Floor New York NY 10016 USA

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and
L. Zajíček Charles University Faculty of Mathematics and Physics Sokolovská 83 186 75 Praha 8-Karlín Czech Republic

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Pages:
85–111
Online Publication Date:
13 Apr 2010
Publication Date:
01 Apr 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-010-9094-x
Keywords:
curve in Banach spaces; parametrization with a Hölder derivative; differentiability via homeomorphisms; primary 26E20; secondary 26A51, 53A04
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Abstract  

Let X be a Banach space and α ∈ (0, 1]. We find equivalent conditions for a function f: [0,1] → X to admit an equivalent parametrization, which is C1,α (i.e., has α-Hölder derivative). For X = ℝ, a characterization is well-known. However, even in the case X = ℝ2 several new ideas are needed.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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