Maximal function and Carleson measures in the theory of Békollé-Bonami weights

Carnot D. Kenfack; Benoît F. Sehba

Colloquium Mathematicae, Tome 144 (2016), p. 211-226 / Harvested from The Polish Digital Mathematics Library

Résumé

Let ω be a Békollé-Bonami weight. We give a complete characterization of the positive measures μ such that $\int_{} | M_{ω} {f (z) |}^{q} d μ (z) \leq C (\int_{} {| f (z) |}^{p} {ω (z) d V (z))}^{q / p}$ and $μ (z \in : M f (z) > λ) \leq C / (λ^{q}) (\int_{} | f (z) {|^{p} ω (z) d V (z))}^{q / p}$ , where $M_{ω}$ is the weighted Hardy-Littlewood maximal function on the upper half-plane and 1 ≤ p,q <; ∞.

Publié le : 2016-01-01

Zbl 1334.42041

EUDML-ID : urn:eudml:doc:286345

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     author = {Carnot D. Kenfack and Beno\^\i t F. Sehba},
     title = {Maximal function and Carleson measures in the theory of B\'ekoll\'e-Bonami weights},
     journal = {Colloquium Mathematicae},
     volume = {144},
     year = {2016},
     pages = {211-226},
     zbl = {1334.42041},
     language = {en},
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Carnot D. Kenfack; Benoît F. Sehba. Maximal function and Carleson measures in the theory of Békollé-Bonami weights. Colloquium Mathematicae, Tome 144 (2016) pp. 211-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-4/