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).
@article{urn:eudml:doc:41303,
title = {Norm inequalities for the minimal and maximal operator, and differentiation of the integral.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {577-604},
mrnumber = {MR1485505},
zbl = {0903.42007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41303}
}
Cruz-Uribe, David; Neugebauer, Christoph J.; Olesen, Victor. Norm inequalities for the minimal and maximal operator, and differentiation of the integral.. Publicacions Matemàtiques, Tome 41 (1997) pp. 577-604. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41303/