Resumen de Two weight inequalities for positive operators: doubling cubes

Wei Chen, Michael T. Lacey

• For the maximal operator M on Rd, and 1

  ∫QM(σ1Q)pdw≲σ(Q), for all cubes Q for which there is a cube P⊃Q satisfying σ(P)≤Dσ(Q), and ℓ(P)≥ρℓ(Q). This was recently proved by Kangwei Li and Eric Sawyer. We give a short proof, which is easily seen to hold for several closely related operators.