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Lp–Lrestimates for the Poisson semigroup on homogeneous trees

Part of: Groups and semigroups of linear operators, their generalizations and applications Difference and functional equations Abstract harmonic analysis Difference equations

Published online by Cambridge University Press:  09 April 2009

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

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Let be a homogeneous tree of degree at least three. In this paper we investigate for which values of p and r the (σθ)-Poisson semigroup is Lp – Lr,-bounded, and we sharp estimate for the corresponding operator norms.

Keywords

Homogeneous treesPoisson semigroupsspherical analysis.

MSC classification

Secondary: 43A85: Analysis on homogeneous spaces 47D03: Groups and semigroups of linear operators 39A12: Discrete version of topics in analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 20 - 32
Copyright
Copyright © Australian Mathematical Society 1998

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