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Norm inequalities for the minimal and maximal operator, and differentiation of the integral.

David Cruz-Uribe;  Christoph J. Neugebauer;  Victor Olesen — 1997

Publicacions Matemàtiques

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

Neugebauer, Christoph J. — 2003

Nonlinear Analysis, Function Spaces and Applications

If E ( f ) = { x : lim sup f ☆ μ j ( x ) > lim inf f ☆ μ j ( x ) } , we examine the type of convergence of g k to f so that | E ( g k ) | ≤ M , k = 1 , 2 , ⋯ , implies | E ( f ) | ≤ M .

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