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- W4320342220 abstract "Let $mathbb T_{q+1}$ denote the homogeneous tree of degree $q+1$ with the standard graph distance $d$ and the canonical flow measure $mu$. The metric measure space $(mathbb T_{q+1},d,mu)$ is of exponential growth. Let $mathcal{L}$ denote the flow Laplacian, which is a probabilistic Laplacian self-adjoint on $L^2(mu)$. In this note, we prove some weighted $L^1$-estimates for the heat kernel associated with $mathcal{L}$ and its gradient. As a consequence, we show that the first order Riesz transform associated with the flow Laplacian on $mathbb T_{q+1}$ is bounded on $L^p(mu)$, for $p in (1,2]$ and of weak type $(1,1)$. The latter result was proved in a previous paper by Hebisch and Steger: we give a different proof that might pave the way to further generalizations." @default.
- W4320342220 created "2023-02-13" @default.
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- W4320342220 date "2022-10-13" @default.
- W4320342220 modified "2023-09-26" @default.
- W4320342220 title "Heat kernel and Riesz transform for the flow Laplacian on homogeneous trees" @default.
- W4320342220 doi "https://doi.org/10.48550/arxiv.2210.07148" @default.
- W4320342220 hasPublicationYear "2022" @default.
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