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Journal of Fourier Analysis and Applications

, Volume 18, Issue 2, pp 240–265 | Cite as

Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets

  • Ricardo A. SáenzEmail author
Article
  • 93 Downloads

Abstract

In this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation
$$\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,$$
where K is a p.c.f. set and Δ its Laplacian given by a regular harmonic structure. In particular, we prove the existence of nontangential limits of the corresponding Poisson integrals, and the analogous results of the classical Fatou theorems for bounded and nontangentially bounded harmonic functions.

Keywords

Fractals P.c.f. sets Poisson integrals Boundary behavior of harmonic functions 

Mathematics Subject Classification (2000)

28A80 31B2 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Facultad de CienciasUniversidad de ColimaColimaMexico

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