Weighted norm inequalities on graphs
Résumé
Let $(\Gamma,\mu)$ be an infinite graph endowed with a reversible Markov kernel $p$ and let $P$ be the corresponding operator. We also consider the associated discrete gradient $\nabla$. We assume that $\mu$ is doubling, a uniform lower bound for $p(x,y)$ when $p(x,y)>0$, and gaussian upper estimates for the iterates of $p$. Under these conditions (and in some cases assuming further some Poincaré inequality) we study the comparability of $(I-P)^{1/2} f$ and $\nabla f$ in Lebesgue spaces with Muckenhoupt weights. Also, we establish weighted norm inequalities for a Littlewood-Paley-Stein square function, its formal adjoint, and commutators of the Riesz transform with bounded mean oscillation functions.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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