# Analysis Seminar on Friday April 21, 3:30-4:30pm, SMLC 356 (to be confirmed)

### Event Description:

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*Title: **Poisson integrals and maximal functions*

#### Speaker: Ricardo A. Sáenz (Universidad de Colima, Mexico)

Abstract: Given a harmonic structure on an post-critically finite set *K*, and its induced Laplacian, we can define the Poisson kernel as the fundamental solution to the Poisson equation on R+ x K, with either Dirichlet or Neumann boundary conditions. The corresponding Poisson integrals satisfy many of the properties of the classical integrals on R+ x R^n, in particular, the existence of boundary limits, both vertical and nontangential. In this talk we discuss these properties, and we also discuss the maximal functions of Poisson integrals and the Hardy spaces determined by them.