We consider a homogeneous tree endowed with a nondoubling flow measure μ of exponential growth and a probabilistic Laplacian L self-adjoint with respect to μ. We prove that the maximal characterization in terms of the heat and the Poisson semigroup of L and the Riesz transform characterization of the atomic Hardy space introduced in a previous work fail.
Hardy spaces on homogeneous trees with flow measures
Santagati F.
2022-01-01
Abstract
We consider a homogeneous tree endowed with a nondoubling flow measure μ of exponential growth and a probabilistic Laplacian L self-adjoint with respect to μ. We prove that the maximal characterization in terms of the heat and the Poisson semigroup of L and the Riesz transform characterization of the atomic Hardy space introduced in a previous work fail.
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