Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs - Suying Liu (MDPI AG, 2021)
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.