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The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts. We show here that the same is true in any Rn —the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new one

Why the Riesz transforms are averages of the dyadic shifts?