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arXiv · 1411.3352

Hardy and BMO spaces on graphs, application to Riesz transform

Joseph Feneuil
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Abstract

Let $Γ$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $Γ$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these spaces. We also characterize the dual space of $H^1$ as a $BMO$-type space adapted to $P$. As an application, we establish $H^1$-$H^1$ and $H^1$-$L^1$ boundedness of the Riesz transform.

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Joseph Feneuil. 2014-10-24. Hardy and BMO spaces on graphs, application to Riesz transform. https://doi.org/10.1007/s11118-016-9533-6

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