Sharp weighted bounds for the q‐variation of singular integrals

By Tuomas Hytönen, Michael T. Lacey, C. P'erez. 2012

139 citations recorded by the source corpus.

We extend the sharp weighted bound of the A2 theorem to the q‐variation norm of certain Calderón–Zygmund operators (q>2), a stronger nonlinearity than the maximal truncations that have been treated before. We obtain this result by a new non‐probabilistic approach that was independently discovered by Lerner.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1cf5bc46322f150ef3b86427c73f6b75d74023d

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In Applied Mathematics

1. Tuomas Hytönen
2. Andrei K. Lerner
3. Michael T. Lacey
4. D. Cruz-Uribe
5. Kabe Moen
6. C. P'erez
7. Kangwei Li
8. Dachun Yang

In Mathematical Physics

1. Tuomas Hytönen
2. D. Cruz-Uribe
3. Andrei K. Lerner

Citations in the corpus

• The two‐weight inequality for the Hilbert transform with general measures (2018, background): “K|.) For definiteness, let Iu(K) := ∅if such an interval does not exist. We need the following geometric result, which is essentially [4, Lemma 2.5], and can be proven in the same way. Lemma 6.2 ((cf. [4], Lemma 2.5)). For every K and j ≥ 1, we have at least two values of u such that Iu(K) ⊃ 3K, and ”
• Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, methodology): “The approach to the q-variation in [19] was through a non-probabilistic counterpart of the Dyadic Representation, a Dyadic Domination, which was independently discovered by Lerner [26, 27].”