Hardy and BMO spaces on graphs, application to Riesz transform

Joseph Feneuil (1)

1 IF - Institut Fourier

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.

Mots clés: BMO; Hardy space; Gaffney estimates; Riesz transform; Differential forms; Graph

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Joseph Feneuil. Hardy and BMO spaces on graphs, application to Riesz transform. Potential Analysis, 2016, 45 (1), pp.1-54. ⟨10.1007/s11118-016-9533-6⟩. ⟨hal-01074559⟩