Mixed weak type estimates: Examples and counterexamples related to a   problem of E. Sawyer
  We study mixed weighted weak-type inequalities for families of functions, which can be applied to study classical operators in harmonic analysis. Our main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C. Perez, Weighted weak-type inequalities and a conjecture of Sawyer, Int. Math. Res. Not., V. 30, 2005, 1849-1871. 
Carlos Perez and Sheldy Ombrosi
math.CA