Hölder's inequality

It has a number of generalizations, among them Hölder's inequality.

A paraproduct may also be required to satisfy some form of Hölder's inequality.

Young's inequality for products can be used to prove Hölder's inequality.

The brief statement of Hölder's inequality uses some conventions.

Writing the equation as , and using the Hölder's inequality we find .

The latter formulation follows from the former through an application of Hölder's inequality and a duality argument.

Hölder's inequality was first found by , and discovered independently by .

The first paper containing Hölder's inequality.

Conjugate indices are used in Hölder's inequality.

Hölder's inequality.

This yields Hölder's inequality in R:

The results for higher moments follow from Hölder's inequality, which implies that higher moments (or halves of moments) diverge if lower ones do.

This result, known as Jensen's inequality underlies many important inequalities (including, for instance, the arithmetic-geometric mean inequality and Hölder's inequality).

In mathematical analysis Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of L spaces.

We call the inequality in (b) a reverse Hölder inequality as the reverse inequality follows for any non-negative function directly from Hölder's inequality.

Leonard James Rogers FRS (30 March 1862, Oxford, England, - 12 September 1933, Oxford, England) was a British mathematician who was the first to discover the Rogers-Ramanujan identity and Hölder's inequality, and who introduced Rogers polynomials.

In mathematics, the Brascamp-Lieb inequality is a result in geometry concerning integrable functions on n-dimensional Euclidean space R. It generalizes the Loomis-Whitney inequality and Hölder's inequality, and is named after Herm Jan Brascamp and Elliott H. Lieb.