Muckenhoupt Weights

We establish the sufficiency of conditions for certain weighted weak (p,p) inequalities for the maximal operator and fractional maximal operators when p > 1, completing a characterization posed by Muckenhoupt and Wheeden.

We prove multilinear analogs of sharp weighted weak-type bounds for singular integrals in both the change of measure and the multiplier setting. Our results hold for any multilinear operator satisfying a sparse form domination.

We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators.

We obtain new sharp estimates for a family of Carleson sequences related to dyadic $A_2$ weights. The proof uses Bellman functions, but unlike the typical situation found in literature, in our setting these functions do not have infinitesimal extremal splits and do no arise as solutions of a PDE. This is a continuation of the work of the first author.