L^p-L^r estimates for the Poisson semigroup
on homogeneous trees

Alberto G. Setti
Dipartimento di Matematica
Università di Milano
via Saldini 50
20133 Milano
Italy
e-mail: setti@dsdipa.mat.unimi.it

Abstract:

Let $\mathgoth X$ be a homogeneous tree of degree at least three. In this paper we investigate for which values of p and r the $(\sigma,\theta)$-Poisson semigroup is L^p-L^r-bounded, and we give sharp estimates for the corresponding operator norms.

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