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.
@article{urn:eudml:doc:41201,
title = {Maximal functions and related weight classes.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {127-155},
mrnumber = {MR1291957},
zbl = {0821.42013},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41201}
}
Sbordone, Carlo; Wik, Ingemar. Maximal functions and related weight classes.. Publicacions Matemàtiques, Tome 38 (1994) pp. 127-155. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41201/