Maximal functions and related weight classes.

Sbordone, 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 -