The Riesz $R_i$ transform on $\mathbb{R}^n$ is defined by $$ R_if(x)= \int_{\mathbb{R}^n} \frac{t_ix_i}{\vert xt \vert^{n+1}}f(t) dt$$ for a Schwartz function $f$ on $\mathbb{R}^n$. Can you please tell me, how can one show that they admit a bounded extension on $L^2(\mathbb{R}^n)$?
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