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Lerner, Andrei K.; Ombrosi, Sheldy; Rivera-Ríos, Israel P.
Advances in mathematics (New York. 1965), 10/2017, Letnik: 319Journal Article
In recent years, it has been well understood that a Calderón–Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar pointwise estimate for the commutator b,T with a locally integrable function b. This result is applied into two directions. If b∈BMO, we improve several weighted weak type bounds for b,T. If b belongs to the weighted BMO, we obtain a quantitative form of the two-weighted bound for b,T due to Bloom–Holmes–Lacey–Wick.
