On the Gowers U2 and U3 norms of Boolean functions and their restriction to hyperplanes

It is known that the smaller the values of Gowers U2 and U3 norms of a Boolean function, the greater its strength against linear and quadratic approximations. This article gives recursive relation between the Gowers U2 and U3 norms of Boolean functions and their restriction to hyperplanes. These results will help analyze the second and third-order Gowers norms of Boolean functions in a higher number of variables. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This article investigates the recursive relation between the Gowers U2 and U3 norms of Boolean functions and their restriction to hyperplanes, which aids in analyzing the second and third-order Gowers norms of Boolean functions in a higher number of variables.