# What is the justification for this inequality?

Homework Helper
Gold Member
What is the justification for this inequality?

$$\int_0^1(|u(s)|+|v(s)|)(|u(s)|-|v(s)|)ds\leq \left(\int_0^1(|u(s)|^2+|v(s)|^2)ds\right)^{1/2}\left(\int_0^1(|u(s)-v(s)|^2)ds\right)^{1/2}$$

where u and v are complex-valued square-integrable Riemann integrable functions on [0,1].

Thx.