On some properties of dyadic operators (Q2154935)

In this paper, the authors investigate dyadic operators, like, in particular, paraproducts, Haar multipliers, and dyadic shifts. After a nice historical introduction with a useful list of old and recent results on this topic, the authors study the continuity properties of dyadic operators. Then they ask whether dyadic operators are compact or not, and in almost all cases provide a negative answer to this question. The authors also notice that, even if dyadic operators are not compact in general, it turns out that their commutators and iterated commutators may be compact.