$L_p$ regular sparse hypergraphs: box norms
Tom 248 / 2020
Fundamenta Mathematicae 248 (2020), 49-77
MSC: Primary 05C35, 05C65; Secondary 46B20, 46B25.
DOI: 10.4064/fm656-10-2018
Opublikowany online: 17 June 2019
Streszczenie
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.
