Characterisations of function spaces on fractals

This thesis consists of three papers, all of them on the topic of function spaces on fractals. The first paper deals with piecewise continuous wavelets of higher order in Besov spaces defined on fractals. In the second paper we compare differently defined function spaces on the Sierpinski gasket. R. S. Strichartz proposes a discrete definition of Besov spaces of continuous functions on self-similar fractals having a regular harmonic structure. The last paper gives a discrete characterisation of certain Lipschitz spaces on a class of fractal sets…


1 Introduction
1.1 Fractals: a non-technical introduction for everyone
1.2 Fractals and function spaces on fractals
1.3 Notes and reference
2 Summary of papers
2.1 Paper I: Wavelets and Besov spaces on Mauldin-Williams fractals
2.2 Paper II: Harmonic functions and Lipschitz spaces on the Sierpinski gasket
2.3 Paper III: A discrete characterisation of Lipschitz spaces on fractals…

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