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On weak type inequalities for rare maximal functions. (English) Zbl 1030.42017

Summary: 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.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
26D15 Inequalities for sums, series and integrals
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