Open Access
2009 Singular integrals on Sierpinski gaskets
V. Chousionis
Publ. Mat. 53(1): 245-256 (2009).


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 $L^2(\mu_d)$ and their principal values diverge $\mu_d$ almost everywhere, where $\mu_d$ is the natural ($d$-dimensional) measure on $E_d$.


Download Citation

V. Chousionis. "Singular integrals on Sierpinski gaskets." Publ. Mat. 53 (1) 245 - 256, 2009.


Published: 2009
First available in Project Euclid: 17 December 2008

zbMATH: 1153.42005
MathSciNet: MR2474123

Primary: 42B20

Keywords: self similar sets , singular integrals

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 1 • 2009
Back to Top