Article Dans Une Revue Publicacions Matemàtiques Année : 2009

Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs

Résumé

Let $\Gamma$ be a graph endowed with a reversible Markov kernel $p$, and $P$ the associated operator, defined by $Pf(x)=\sum_y p(x,y)f(y)$. Denote by $\nabla$ the discrete gradient. We give necessary and/or sufficient conditions on $\Gamma$ in order to compare $\left\Vert \nabla f\right\Vert_{p}$ and $\left\Vert (I-P)^{1/2}f\right\Vert_{p}$ uniformly in $f$ for $12$. The proofs rely on recent techniques developed to handle operators beyond the class of Calderón-Zygmund operators. For our purpose, we also prove Littlewood-Paley inequalities and interpolation results for Sobolev spaces in this context, which are of independent interest.

Fichier principal
Vignette du fichier
Rieszgraph.pdf (421.64 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-00243816 , version 1 (07-02-2008)

Licence

Identifiants

Citer

Nadine Badr, Emmanuel Russ. Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs. Publicacions Matemàtiques, 2009, 53 (2), pp.273-328. ⟨hal-00243816⟩
182 Consultations
330 Téléchargements

Altmetric

Partager

  • More