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
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.
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Communicated by Robert Strichartz.
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Sáenz, R.A. Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets. J Fourier Anal Appl 18, 240–265 (2012). https://doi.org/10.1007/s00041-011-9194-1
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DOI: https://doi.org/10.1007/s00041-011-9194-1