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

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

2012-02-10

arxiv.org/abs/1202.2229v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

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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