Representation of singular integrals by dyadic operators, and the A_2 theorem

By Tuomas Hytönen. 2011

49 citations recorded by the source corpus.

. This exposition presents a self-contained proof of the A 2 theo- rem, the quantitatively sharp norm inequality for singular integral operators in the weighted space L 2 ( w ) . The strategy of the proof is a streamlined version of the author’s original one, based on a probabilistic Dyadic Representation Theorem for singular integral operators. While more recent non-probabilistic approaches are also available now, the probabilistic method provides additional structural information, which has independent interest and other applications. The presentation emphasizes connections to the David–Journé T (1) theorem, whose proof is obtained as a byproduct. Only very basic Probability is used; in particular, the conditional probabilities of the original proof are completely avoided.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3c3bd2f5b54acd59161f10e80d103781129de46c

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Uniform sparse domination of singular integrals via dyadic shifts (2016, background): “3 of [12] rewritten in our language yields that for each T ∈ U , f1, f2 ∈ W, the equality”
Commutators in the two-weight setting (2015, methodology): “↑8 [19] T. Hytönen and C. Pérez, Sharp weighted bounds involving A∞, Anal.”