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

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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 Sós (2015) about the relation b...More