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Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Suying Liu & Feng Liu, 2021. "Sobolev Regularity of Multilinear Fractional Maximal Operators on Infinite Connected Graphs," Mathematics, MDPI, vol. 9(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2883-:d:677901
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