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

Autores: C.J. Neugebauer, David Cruz-Uribe , V. Olesen
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 577-604
Idioma: inglés
DOI: 10.5565/publmat_41297_20
Títulos paralelos:
- Desigualdades de norma para los operadores mínimo y máximo, y diferenciación de la integral
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Resumen
- 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)