U does not fade away more weakly than $\frac{1}{\lVert x\rVert^{n-2}}$

Question

Hello I have a function $u$ and it is said that for $n>2$ it does not fade away (in German: abklingen) more weakly than $\frac{1}{\lVert x\rVert^{n-2}}$.

What is meant with that?

I do not know this manner of speaking...

Answer 1

This might mean that $$\lim_{\| x\| \to \infty} \frac{u(x)}{\|x\|^{n-2}} < \infty .$$