Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp $A_2$ estimates of Haar shifts via Bellman function   We use the Bellman function method to give an elementary proof of a sharp
weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the
weight and in the complexity of the shift. Together with the representation of
a general Calder\'{o}n--Zygmund operator as a weighted average (over all dyadic
lattices) of Haar shifts, (cf. arXiv:1010.0755v2[math.CA],
arXiv:1007.4330v1[math.CA]) it gives a significantly simpler proof of the
so-called the $A_2$ conjecture.
  The main estimate is a very general fact about concave functions, which can
be very useful in other problems of martingale Harmonic Analysis. Concave
functions of such type appear as the Bellman functions for bounds on the
bilinear form of martingale multipliers, thus the main estimate allows for the
transference of the results for simplest possible martingale multipliers to
more general martingale transforms.
  Note that (although this is not important for the $A_2$ conjecture for
general Calder\'{o}n--Zygmund operators) this elementary proof gives the best
known (linear) growth in the complexity of the shift.

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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th