BCAM Working Seminar APDE: Sharp constants for maximal operators on finite graphs

Abstract
Let $G$ be a finite graph and $M_{G}$ be its centered Hardy-Littlewood maximal operator defined with respect to the counting measure and the metric induced by the edges. In this talk we will present some recent results concerning the norm $|M_{G}|_{p}$ for $pge 1$ when $G=K_n$ or $S_n$. Also, we will discuss some sharp constants for the $p-$variation of $M_{G}$ when acting on such graphs. Moreover, we will discuss some open questions that arise in this setting. This talk is based on joint work with José Madrid (UCLA) 

Link to the session: https://zoom.us/j/98469566860?pwd=MTFnUENPYUt6QUxMeWFjelpVdFhMQT09