Brascamp–Lieb inequality

The Brascamp–Lieb inequality is an important result in the field of functional analysis and geometric measure theory. It provides a powerful estimate for integrals of products of functions that arise in various areas of mathematics, including harmonic analysis and the theory of partial differential equations. ### Statement of the Inequality The Brascamp–Lieb inequality states that for a collection of measurable functions and linear maps, one can obtain an upper bound on the integral of a product of these functions.