Singular integrals on Sierpinski gaskets

Details Singular integrals on Sierpinski gaskets Singular integrals on Sierpinski gaskets

2008-04-03

arxiv.org/abs/0804.0517v5

Publ. Mat. 53 (2009), no. 1, 245--256

Mathematics

Functional Analysis

Scientific paper

We construct a class of singular integral operators associated with
homogeneous Calder\'{o}n-Zygmund standard kernels on $d$-dimensional, $d <1$,
Sierpinski gaskets $E_d$. These operators are bounded in $L^2(\mu_d)$ and their
principal values diverge $\mu_d$ almost everywhere, where $\mu_d$ is the
natural (d-dimensional) measure on $E_d$.

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