Maximal Operators

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.