Weak spectral equivalence and weak spectral convergence
Why the Riesz transforms are averages of the dyadic shifts?
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.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations,...