Singular integrals on Sierpinski gaskets. (English) Zbl 1153.42005

Chousionis, Vasilis

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

Summary: 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 \(E _d \).

MSC:

42B20

Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Keywords:

singular integrals; self similar sets