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

Cruz-Uribe, David, Neugebauer, Christoph J., and Olesen, Victor. "Norm inequalities for the minimal and maximal operator, and differentiation of the integral.." Publicacions Matemàtiques 41.2 (1997): 577-604. <http://eudml.org/doc/41303>.

@article{Cruz1997,
abstract = {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).},
author = {Cruz-Uribe, David, Neugebauer, Christoph J., Olesen, Victor},
journal = {Publicacions Matemàtiques},
keywords = {Operador maximal de Hardy-Littlewood; Análisis de Fourier; Funciones medibles; weighted norm inequalities; minimal operator; maximal operator; weak type},
language = {eng},
number = {2},
pages = {577-604},
title = {Norm inequalities for the minimal and maximal operator, and differentiation of the integral.},
url = {http://eudml.org/doc/41303},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Cruz-Uribe, David
AU - Neugebauer, Christoph J.
AU - Olesen, Victor
TI - Norm inequalities for the minimal and maximal operator, and differentiation of the integral.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 577
EP - 604
AB - 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).
LA - eng
KW - Operador maximal de Hardy-Littlewood; Análisis de Fourier; Funciones medibles; weighted norm inequalities; minimal operator; maximal operator; weak type
UR - http://eudml.org/doc/41303
ER -