A Littlewood–Paley–Stein estimate on graphs and groups
Tom 189 / 2008
Studia Mathematica 189 (2008), 113-129 MSC: 42B25, 60G50, 60B15. DOI: 10.4064/sm189-2-3
We establish the boundedness in $L^q$ spaces, $1< q\leq 2$, of a “vertical" Littlewood–Paley–Stein operator associated with a reversible random walk on a graph. This result extends to certain non-reversible random walks, including centered random walks on any finitely generated discrete group.