Sharp weighted bounds involving A_\infty

Details Sharp weighted bounds involving A_\infty Sharp weighted bounds involving A_\infty

2011-03-29

arxiv.org/abs/1103.5562v1

Mathematics

Classical Analysis and ODEs

41 pages

Scientific paper

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

Affiliated with

Also associated with

No associations

Rating

Sharp weighted bounds involving A_\infty does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp weighted bounds involving A_\infty, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp weighted bounds involving A_\infty will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162932