weighted inequality of Fourier transform

Question

For $1<p\leq2$, prove that $$\|\hat{f}\|_{L^p(R^n,|x|^{n(p-2)}\quad dx)}\leq C\|f\|_{L^p(R^n,dx)}$$ $\hat{f}$is the Fourier transform of $f$.

It is trivial if $p=2$, I try to use holder inequality but fail. Any idea will be helpful.

Answer 1

Define a operator $T:L^p(R^n,dx)\rightarrow L^p(R^n,|x|^{2n}dx)$ which puts $f$ to $\hat{f}/|x|^n$,then prove it is strong$(2,2)$ and weak(1,1).