# Maximal functions and related weight classes.

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 1, page 127-155
- ISSN: 0214-1493

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topSbordone, Carlo, and Wik, Ingemar. "Maximal functions and related weight classes.." Publicacions Matemàtiques 38.1 (1994): 127-155. <http://eudml.org/doc/41201>.

@article{Sbordone1994,

abstract = {The famous result of Muckenhoupt on the connection between weights w in Ap-classes and the boundedness of the maximal operator in Lp(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the Ap-constants. The equality of two differently defined A∞-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a parallel theory to the Ap-theory is established for the connection between weights in Bp-classes and maximal functions, thereby extending and developing the recent results of Ariño and Muckenhoupt.},

author = {Sbordone, Carlo, Wik, Ingemar},

journal = {Publicacions Matemàtiques},

keywords = {Funciones de peso; Operadores maximales; Operador maximal de Hardy-Littlewood; Muckenhoupt weights; -weights; -weights; - weights; maximal functions; Hardy-Littlewood maximal operator},

language = {eng},

number = {1},

pages = {127-155},

title = {Maximal functions and related weight classes.},

url = {http://eudml.org/doc/41201},

volume = {38},

year = {1994},

}

TY - JOUR

AU - Sbordone, Carlo

AU - Wik, Ingemar

TI - Maximal functions and related weight classes.

JO - Publicacions Matemàtiques

PY - 1994

VL - 38

IS - 1

SP - 127

EP - 155

AB - The famous result of Muckenhoupt on the connection between weights w in Ap-classes and the boundedness of the maximal operator in Lp(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the Ap-constants. The equality of two differently defined A∞-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a parallel theory to the Ap-theory is established for the connection between weights in Bp-classes and maximal functions, thereby extending and developing the recent results of Ariño and Muckenhoupt.

LA - eng

KW - Funciones de peso; Operadores maximales; Operador maximal de Hardy-Littlewood; Muckenhoupt weights; -weights; -weights; - weights; maximal functions; Hardy-Littlewood maximal operator

UR - http://eudml.org/doc/41201

ER -

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