Hardy-Littlewood maximal operators on graphs with bounded geometry

Tuesday, 23-July-2024 

Abstract

 In this talk, we discuss the $L^p$ boundedness of the centred and the uncentred Hardy–Littlewood maximal operators on the class of trees with $(a,b)$-bounded geometry, i.e., trees such that every vertex has at least $a+1$ and at most $b+1$ neighbours. We provide the sharp range of $p$, depending on $a$ and $b$, for which the centred maximal operator is bounded on $L^p$. We also extend these results to graphs that are roughly isometric, in the sense of Kanai, to trees with bounded geometry. This is based on joint work with M. Levi, S. Meda, and M. Vallarino.