- #1

- 1,104

- 945

Take a function ##f\in C(\mathbb{R}^3)\cap L^1(\mathbb{R}^3)## and a number ##\alpha\in(0,3)##.

Prove that

$$\lim_{|x|\to\infty}\int_{\mathbb{R}^3}\frac{f(y)dy}{|x-y|^\alpha}=0.$$

I can prove this fact by the Uniform Boundedness Principle only. This frustrates me much.