Find in dependance of an $\varepsilon > 0 $ and $p \in (1, \infty)$ a $C_{\varepsilon} > 0$ with:
\begin{equation} ||s-t|^p-|t|^p-|s|^p|\le \varepsilon |t|^p+C_{\varepsilon} |s|^p \end{equation} for all $s, t \in \mathbb{R}$. In case of $|t|<|s|$ set $\nu=t/s$.
We don't know about Young's inequality yet. I really don't know how to start at all. Can you give me some advice what I can use. Thank you.