The properties of rare maximal functions (i.e. Hardy-Littlewood maximal functions associated with sparse families of intervals) are investigated. A simple criterion allows one to decide if a given rare maximal function satisfies a converse weak type inequality. The summability properties of rare maximal functions are also considered.
@article{bwmeta1.element.bwnjournal-article-cmv83i2p173bwm, author = {K. Hare and A. Stokolos}, title = {On weak type inequalities for rare maximal functions}, journal = {Colloquium Mathematicae}, volume = {84/85}, year = {2000}, pages = {173-182}, zbl = {1030.42017}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p173bwm} }
Hare, K.; Stokolos, A. On weak type inequalities for rare maximal functions. Colloquium Mathematicae, Tome 84/85 (2000) pp. 173-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i2p173bwm/
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