Weighted norm inequalities for averaging operators of monotone functions.
We prove weighted norm inequalities for the averaging operator Af(x) = 1/x ∫ f of monotone functions.
Homeomorphisms preserving A.
Weighted norm inequalities for the geometric maximal operator.
Norm inequalities for the minimal and maximal operator, and differentiation of the integral.
We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We 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. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the...
Transmission of convergence
If , we examine the type of convergence of to so that , , implies .
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