Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs

Suying Liu and Feng Liu
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Suying Liu: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China
Feng Liu: College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2021, vol. 9, issue 22, 1-19

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 Haj?asz–Sobolev spaces on G .

Keywords: infinite connected graph; multilinear fractional maximal operator; endpoint Sobolev regularity; Haj?asz–Sobolev space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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