A characterization of functions with vanishing averages over products of disjoint sets

@article{Hatami2016ACO,
title={A characterization of functions with vanishing averages over products of disjoint sets},
author={Hamed Hatami and P. Hatami and Yaqiao Li},
journal={Eur. J. Comb.},
year={2016},
volume={56},
pages={81-93}
}

Given α 1 , � , α m � ( 0 , 1 ) , we characterize all integrable functions f : 0 , 1 m � C satisfying � A 1 � � � A m f = 0 for any collection of disjoint measurable sets A 1 , � , A m � 0 , 1 of respective measures α 1 , � , α m . We use this characterization to settle some of the conjectures in Janson and Sos (2015) about the relation between subgraph counts and quasi-randomness.