  In this article we derive quantitative uniqueness and approximation
properties for (perturbations) of Riesz transforms. Seeking to provide robust
arguments, we adopt a PDE point of view and realize our operators as harmonic
extensions, which makes the problem accessible to PDE tools. In this context we
then invoke quantitative propagation of smallness estimates in combination with
qualitative Runge approximation results. These results can be viewed as
quantifications of the approximation properties which have recently gained
prominence in the context of nonlocal operators, c.f. [DSV14], [DSV16].
