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

Nadine Badr, Emmanuel Russ

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…