Boolean Functions with Small Second-Order Influences on the Discrete Cube

Abstract

Motivated by a recent paper of Tanguy (J Theoret Probab 33:692–714, 2020), in which the concept of second-order influences on the discrete cube and Gauss space has been investigated in detail, the present note studies it in a more specific context of Boolean functions on the discrete cube. Some bounds that Tanguy obtained in Tanguy (J Theoret Probab 33:692–714, 2020) as applications of his more general approach are extended and complemented.