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

Hamed Hatami, Pooya Hatami, Yaqiao Li

Given ${\alpha }_1,...,{\alpha }_m\in (0,1)$, we characterize all integrable functions $f:[0,1{]}^m\to \mathbb{C}$ satisfying ${\int }_{A_1\times ...\times A_m}f=0$ for any collection of disjoint…