Here I encounter a problem when I want to derive Riesz transform:
For $f(x)\in\mathcal{L}^p,1<p<\infty.$ We know the Fourier transform of Riesz transform: $$\widehat{R_jf}=\frac{\xi_j}{|\xi|}\hat{f}.$$ We set the notion of Fourier transform of $f$ by: $$\hat{f}(\xi)=\int_{\mathbb{R}^{n}} e^{-ix\xi}f(x)\text{d}x.$$
Then how to derive Riesz transform only given the Fourier transform of Riesz transform?