TY - JOUR TI - Lp regular sparse hypergraphs: Box norms AU - Dodos, P. AU - Kanellopoulos, V. AU - Karageorgos, T. JO - Fundamenta Mathematicae PY - 2020 VL - 248 TODO - 1 SP - 49-77 PB - Institute of Mathematics. Polish Academy of Sciences SN - 0016-2736, 1730-6329 TODO - 10.4064/fm656-10-2018 TODO - null TODO - 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 Lp 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. © Instytut Matematyczny PAN, 2020. ER -