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$L_p$ regular sparse hypergraphs: box norms

Volume 248 / 2020

Pandelis Dodos, Vassilis Kanellopoulos, Thodoris Karageorgos Fundamenta Mathematicae 248 (2020), 49-77 MSC: Primary 05C35, 05C65; Secondary 46B20, 46B25. DOI: 10.4064/fm656-10-2018 Published online: 17 June 2019

Abstract

We consider some variants of the Gowers box norms, introduced by Hatami, and show their relevance in the context of sparse hypergraphs. Our main results are the following. Firstly, we prove a generalized von Neumann theorem for $L_p$ graphons. Secondly, we give natural examples of pseudorandom families, that is, sparse weighted uniform hypergraphs which satisfy relative versions of the counting and removal lemmas.

Authors

  • Pandelis DodosDepartment of Mathematics
    University of Athens
    Panepistimiopolis
    157 84 Athens, Greece
    e-mail
  • Vassilis KanellopoulosNational Technical University of Athens
    Faculty of Applied Sciences
    Department of Mathematics
    Zografou Campus
    157 80 Athens, Greece
    e-mail
  • Thodoris KarageorgosDepartment of Mathematics
    University of Athens
    Panepistimiopolis 157 84
    Athens, Greece
    e-mail

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