Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs

Abstract

Let G be an infinite connected graph. We introduce two kinds of multilinear fractional maximal operators on G. By assuming that the graph G satisfies certain geometric conditions, we establish the bounds for the above operators on the endpoint Sobolev spaces and Hajłasz–Sobolev spaces on G.

Keywords

• infinite connected graph
• multilinear fractional maximal operator
• endpoint Sobolev regularity
• Hajłasz–Sobolev space