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arXiv · 1202.2229

Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals

Tuomas P. Hytönen·Michael T. Lacey·Carlos Pérez
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Abstract

Any Calderon-Zygmund operator T is pointwise dominated by a convergent sum of positive dyadic operators. We give an elementary self-contained proof of this fact, which is simpler than the probabilistic arguments used for all previous results in this direction. Our argument also applies to the q-variation of certain Calderon-Zygmund operators, a stronger nonlinearity than the maximal truncations. As an application, we obtain new sharp weighted inequalities.

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Tuomas P. Hytönen, Michael T. Lacey, Carlos Pérez. 2012-02-10. Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals. https://doi.org/10.1112/blms%2Fbds114

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