Hardy spaces on homogeneous trees with flow measures

Abstract

We consider a homogeneous tree endowed with a nondoubling flow measure $\mu$ of exponential growth and a probabilistic Laplacian $\mathcal{L}$ self-adjoint with respect to $\mu$. We prove that the maximal characterization in terms of the heat and the Poisson semigroup of $\mathcal{L}$ and the Riesz transform characterization of the atomic Hardy space introduced in a previous work fail.

24 pages

References in corpus (3)

• Analysis on trees with nondoubling flow measures
• Riesz transform for a flow Laplacian on homogeneous trees
• Maximal characterisation of local Hardy spaces on locally doubling manifolds

Cited by in corpus (1)

• Riesz transform for a flow Laplacian on homogeneous trees