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Zbl 1166.42019
Jaffard, Stéphane
Wavelet techniques for pointwise regularity. (English)
[J] Ann. Fac. Sci. Toulouse, Math. (6) 15, No. 1, 3-33 (2006). ISSN 0240-2963

Let $E$ be a shift and scaling invariant Banach or quasi-Banach space. This paper introduces a general definition of pointwise regularity $C^{\alpha}_E(x_0)$ associated with $E$. Then it shows that how properties of $E$ are transferred into properties of $C^{\alpha}_E(x_0)$ in terms of wavelet characterizations. The application to multifractal analysis is investigated.
[Lizhong Peng (Beijing)]

MSC 2000:: *42C40 Wavelets
28A80 Fractals
46E30 Spaces of measurable functions

Keywords: Banach space; quasi-Banach space; pointwise regularity; wavelet; multifractal analysis

Cited in: Zbl 1230.46030

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