$|f(x)|\leq |g(x)|$, $g$ is radial

Question

Let $f\in L^p(\mathbb{R}^d)$, where $1\leq p < \infty$, and $d \in \mathbb{N}$.

Then does there exist $r>0$ and a radial function $g\in L^p(B_r)$ ($g(x)=g(|x|), x\in B_r=\{x\in \mathbb{R}^d;|x|<r \}$) such that

$|f(x)|\leq |g(x)| \ a.e. x \in B_r$?