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Analysis of $L^p$-type estimates of Poisson transform on Homogeneous Trees

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arxiv 1808.09659 v1 pith:YWR5FSTS submitted 2018-08-29 math.FA

Pratyoosh Kumar , Sumit Kumar Rano This is my paper · ORCID
classification math.FA
keywords transformhomogeneouspoissonestimatestreeanalysisargumentarticle
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abstract

In this article we prove the restriction theorem for Helgason-Fourier transform on homogeneous tree. Our proof is based on the duality argument and the norm estimates of Poisson transform. We also characterize all eigenfunctions of the laplacian on homogeneous tree which are Poisson transform of $L^p$ functions defined on the boundary.

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  1. A Theorem of Roe and Strichartz on homogeneous trees

    math.FA 2019-08 conditional novelty 5.0 of 10

    Weak L^p bounds on all integer powers of the Laplacian on a homogeneous tree force the function to be a Laplacian eigenfunction.

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