About a property equivalent to Ap weight condition for the Hardy-Littlewood maximal operator
Abstract
The inequality Mf (x)p C Mw (j f jp) (x), for a weight function w, is a consequence of the weak type (p; p) for the Hardy-Littlewood maximal operator from Lp (w). A recent result shows that the inequality also implies the weak type
(p; p) so, in fact, both conditions are equivalent. Here we give a new an elementary proof of the equivalence that, unlike existing demonstrations, it requires no covering properties.
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References
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