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

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

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 577-604
- ISSN: 0214-1493

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topCruz-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 -

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