We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.
@article{bwmeta1.element.bwnjournal-article-smv101i1p105bwm,
author = {Hugo Aimar and Liliana Forzani},
title = {Weighted weak type inequalities for certain maximal functions},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {105-111},
zbl = {0808.42013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv101i1p105bwm}
}
Aimar, Hugo; Forzani, Liliana. Weighted weak type inequalities for certain maximal functions. Studia Mathematica, Tome 100 (1991) pp. 105-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv101i1p105bwm/
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