JournalsrmiVol. 29, No. 2pp. 433–478

Sharp weak type estimates for weights in the class Ap1,p2A_{p_1, p_2}

  • Alexander Reznikov

    Vanderbilt University, Nashville, USA
Sharp weak type estimates  for weights in the class $A_{p_1, p_2}$ cover
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Abstract

We get sharp estimates for the distribution function of nonnegative weights that satisfy the so-called Ap1,p2A_{p_1, p_2} condition. For particular choices of parameters p1p_1, p2p_2 this condition becomes an ApA_p-condition or reverse Hölder condition. We also get maximizers for these sharp estimates. We use the Bellman technique and try to carefully present and motivate our tactics. As an illustration of how these results can be used, we deduce the following result: if a weight ww is in A2A_2 then it self-improves to a weight that satisfies a reverse Hölder condition.

Cite this article

Alexander Reznikov, Sharp weak type estimates for weights in the class Ap1,p2A_{p_1, p_2}. Rev. Mat. Iberoam. 29 (2013), no. 2, pp. 433–478

DOI 10.4171/RMI/726