Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators

Details Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators

2010-02-10

arxiv.org/abs/1002.2011v1

Mathematics

Functional Analysis

20 pages

Scientific paper

We give the first natural examples of Calder\'on-Zygmund operators in the theory of analysis on post-critically finite self-similar fractals. This is achieved by showing that the purely imaginary Riesz and Bessel potentials on nested fractals with 3 or more boundary points are of this type. It follows that these operators are bounded on $L^{p}$, $1

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