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arXiv · 1002.2011

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

Marius Ionescu·Luke Rogers
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Abstract

We give the first natural examples of Calderón-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 $L^{p}$, $1<p<\infty$ and satisfy weak 1-1 bounds. The analysis may be extended to infinite blow-ups of these fractals, and to product spaces based on the fractal or its blow-up.

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BibTeXRIS

Marius Ionescu, Luke Rogers. 2013-10-31. Complex Powers of the Laplacian on Affine Nested Fractals as Calderón-Zygmund operators. https://arxiv.org/abs/1002.2011

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