Year: 2008
Type: preprint
Abstract: We construct a class of singular integral operators associated with homogeneous Calderón-Zygmund standard kernels on $d$-dimensional, $d <1$, Sierpinski gaskets $E_d$. These operators are bounded in $L^2(μ_d)$ and their principal values diverge $μ_d$ almost everywhere, where $μ_d$ is the natural (d-dimensional) measure on $E_d$.
Source: arXiv (Cornell University)
Author: Chousionis, Vasilis
Institution: University of Helsinki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953274183