Sharp one-weight and two-weight bounds for maximal operators

Kabe Moen. "Sharp one-weight and two-weight bounds for maximal operators." Studia Mathematica 194.2 (2009): 163-180. <http://eudml.org/doc/285364>.

@article{KabeMoen2009,
abstract = {We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm and the testing condition of Sawyer. Finally, our approach leads to a new proof of Buckley's sharp estimate for the Hardy-Littlewood maximal function.},
author = {Kabe Moen},
journal = {Studia Mathematica},
keywords = {maximal function; weights},
language = {eng},
number = {2},
pages = {163-180},
title = {Sharp one-weight and two-weight bounds for maximal operators},
url = {http://eudml.org/doc/285364},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Kabe Moen
TI - Sharp one-weight and two-weight bounds for maximal operators
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 2
SP - 163
EP - 180
AB - We investigate the boundedness of the fractional maximal operator with respect to a general basis on weighted Lebesgue spaces. We characterize the boundedness of these operators for one-weight and two-weight inequalities extending the work of Jawerth. A new two-weight testing condition for the fractional maximal operator on a general basis is introduced extending the work of Sawyer for the basis of cubes. We also find the sharp dependence in the two-weight case between the operator norm and the testing condition of Sawyer. Finally, our approach leads to a new proof of Buckley's sharp estimate for the Hardy-Littlewood maximal function.
LA - eng
KW - maximal function; weights
UR - http://eudml.org/doc/285364
ER -