Norm inequalities for the minimal and maximal operator, and differentiation of the integral (Q1385200)

In this paper, the authors study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which aroses in the study of reverse Hölder inequalities. The authors characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. They also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and they give a new condition for this maximal operator to be of weak type \((1,1)\).