Category:Young's Inequality for Products

This category contains pages concerning Young's Inequality for Products:

Let $p, q \in \R_{> 0}$ be strictly positive real numbers such that:

$\dfrac 1 p + \dfrac 1 q = 1$

Then:

$\forall a, b \in \R_{\ge 0}: a b \le \dfrac {a^p} p + \dfrac {b^q} q$

Equality occurs if and only if:

$b = a^{p - 1}$

Source of Name

This entry was named for William Henry Young.