Hölder's inequality [SEP] named after
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 spaces.
The numbers and above are said to be Hölder conjugates of each other. The special case gives a form of the Cauchy–Schwarz inequality. Hölder's inequality holds even if is infinite, the right-hand side also being infinite in that case. Conversely, if   is in and is in , then the pointwise product is in .
Young's inequality for products
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. The inequality is named after William Henry Young and should not be confused with Young's convolution inequality.
Young's inequality for products can be used to prove Hölder's inequality. It is also widely used to estimate the norm of nonlinear terms in PDE theory, since it allows one to estimate a product of two terms by a sum of the same terms raised to a power and scaled.