Hölder's inequality

Hölder's inequality is a fundamental mathematical tool that compares the sizes of sums or integrals of products of two functions. It states that the combined size (or norm) of the product of two functions is at most the product of their individual sizes, each measured in different ways called Lp-norms. This inequality helps to analyze how functions interact and is widely used in areas like analysis and probability, ensuring that the product of functions stays manageable under certain conditions. Essentially, it provides a bound that guarantees the combined behavior of functions remains controlled within specific mathematical limits.