Variation Inequalities for the Hardy-Littlewood Maximal Function on Finite Directed Graphs

Abstract

In this paper, the authors establish the bounds for the Hardy-Littlewood maximal operator defined on a finite directed graph G→ in the space BVp(G→) of bounded p-variation functions. More precisely, the authors obtain the BVp norms of MG→ for some directed graphs G→.

Keywords

• finite directed graph
• Hardy–Littlewood maximal operator
• bounded variation