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Norm inequalities for the minimal and maximal operator, and differentiation of the integral
Cruz-Uribe, D.
Neugebauer, C. J.
Olesen, V.

Data: 1997
Resum: 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 integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1).
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 41 n. 2 (1997) p. 577-604, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_41297_20

28 p, 215.1 KB

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