Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
@article{bwmeta1.element.bwnjournal-article-smv110i2p149bwm, author = {S. Bloom and R. Kerman}, title = {Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator}, journal = {Studia Mathematica}, volume = {108}, year = {1994}, pages = {149-167}, zbl = {0813.42014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p149bwm} }
Bloom, S.; Kerman, R. Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator. Studia Mathematica, Tome 108 (1994) pp. 149-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv110i2p149bwm/
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