Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp weighted bounds involving A_\infty   We improve on several weighted inequalities of recent interest by replacing a
part of the A_p bounds by weaker A_\infty estimates involving Wilson's A_\infty
constant \[ [w]_{A_\infty}':=\sup_Q\frac{1}{w(Q)}\int_Q M(w\chi_Q). \] In
particular, we show the following improvement of the first author's A_2 theorem
for Calder\'on-Zygmund operators T: \[\|T\|_{B(L^2(w))}\leq c_T
[w]_{A_2}^{1/2}([w]_{A_\infty}'+[w^{-1}]_{A_\infty}')^{1/2}. \] Corresponding
A_p type results are obtained from a new extrapolation theorem with appropriate
mixed A_p-A_\infty bounds. This uses new two-weight estimates for the maximal
function, which improve on Buckley's classical bound. We also derive mixed
A_1-A_\infty type results of Lerner, Ombrosi and the second author (Math. Res.
Lett. 2009) of the form: \[\|T\|_{B(L^p(w))} \leq c
pp'[w]_{A_1}^{1/p}([w]_{A_{\infty}}')^{1/p'}, 1<p<\infty, \]
\[\|Tf\|_{L^{1,\infty}(w)} \leq c[w]_{A_1} \log(e+[w]'_{A_{\infty}})
\|f\|_{L^1(w)}. \] An estimate dual to the last one is also found, as well as
new bounds for commutators of singular integrals.

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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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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: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph