Possible Duplicate:
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
We can use Young's inequality to show that $(a+b)^2 \leq 2a^2 + 2b^2$.
Does a similar result hold for the n-th power as well? That is, do we have $(a + b)^n \leq c_1 a^n + c_2 b^n$ ?
If so, what are the values for $c_1$ and $c_2$?