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September, 2006 How smooth is almost every function in a Sobolev space?
Aurélia Fraysse , Stéphane Jaffard
Rev. Mat. Iberoamericana 22(2): 663-682 (September, 2006).

Abstract

We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

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Aurélia Fraysse . Stéphane Jaffard . "How smooth is almost every function in a Sobolev space?." Rev. Mat. Iberoamericana 22 (2) 663 - 682, September, 2006.

Information

Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1155.28302
MathSciNet: MR2294793

Subjects:
Primary: 26A15 , 26A21 , 28A80 , 28C20 , 46E35
Secondary: ‎42C40 , 54E52

Keywords: Besov spaces , Haar-null sets , Hausdorff dimension , Hölder regularity , multifractal functions , prevalence , Sobolev Spaces , Wavelet bases

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.22 • No. 2 • September, 2006
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