Hardy and BMO spaces on graphs, application to Riesz transform
Résumé
Let $\Gamma$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $\Gamma$. 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 $H^1$ and $H^1$ -$L^1$ boundedness of the Riesz transform.
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