Directed porosity on conformal iterated function systems and weak convergence of singular integrals

Details Directed porosity on conformal iterated function systems and weak convergence of singular integrals Directed porosity on conformal iterated function systems and weak convergence of singular integrals

2008-04-03

arxiv.org/abs/0804.0518v6

Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 215--232

Mathematics

Dynamical Systems

Scientific paper

The aim of the present paper is twofold. We study directed porosity in connection with conformal iterated function systems (CIFS) and with singular integrals. We prove that limit sets of finite CIFS are porous in a stronger sense than already known. Furthermore we use directed porosity to establish that truncated singular integral operators, with respect to general Radon measures $\mu$ and kernels $K$, converge weakly in some dense subspaces of $L^2(\mu)$ when the support of $\mu$ belongs to a broad family of sets. This class contains many fractal sets like CIFS's limit sets.

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