Young's Inequality
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the term Young's inequality is used for two inequalities: one about the product of two numbers, and one about the convolution of two functions. They are named for William Henry Young.Equality holds if and only if ap = bq. Young's inequality is a special case of the inequality of weighted arithmetic and geometric means.Young's inequality is used in the proof of Hölder's inequality. It is also used widely to estimate the norm of nonlinear terms in PDE theory, since it allows one to estimate a...
High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, the term Young's inequality is used for two inequalities: one about the product of two numbers, and one about the convolution of two functions. They are named for William Henry Young.Equality holds if and only if ap = bq. Young's inequality is a special case of the inequality of weighted arithmetic and geometric means.Young's inequality is used in the proof of Hölder's inequality. It is also used widely 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.An example application is that Young's inequality can be used to show that the heat semigroup is a contraction semigroup using the L2 norm.
