Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators

Qingying Xue

Qingying Xue

Studia Mathematica, Tome 215 (2013), p. 97-122 / Harvested from The Polish Digital Mathematics Library

Résumé

The following iterated commutators $T_{*, Π b}$ of the maximal operator for multilinear singular integral operators and $I_{α, Π b}$ of the multilinear fractional integral operator are introduced and studied: $T_{*, Π b} (f ⃗) (x) = s u p_{δ > 0} | [b ₁, [b ₂, \dots {[b_{m - 1}, [b ₘ, T_{δ}] ₘ]}_{m - 1} \dots] ₂] ₁ (f ⃗) (x) |$ , $I_{α, Π b} (f ⃗) (x) = [b ₁, [b ₂, \dots {[b_{m - 1}, [b ₘ, I_{α}] ₘ]}_{m - 1} \dots] ₂] ₁ (f ⃗) (x)$ , where $T_{δ}$ are the smooth truncations of the multilinear singular integral operators and $I_{α}$ is the multilinear fractional integral operator, $b_{i} \in B M O$ for i = 1,…,m and f⃗ = (f1,…,fm). Weighted strong and L(logL) type end-point estimates for the above iterated commutators associated with two classes of multiple weights, $A_{p ⃗}$ and $A_{(p ⃗, q)}$ , are obtained, respectively.

Publié le : 2013-01-01

Zbl 1321.42038

EUDML-ID : urn:eudml:doc:285816

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     author = {Qingying Xue},
     title = {Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators},
     journal = {Studia Mathematica},
     volume = {215},
     year = {2013},
     pages = {97-122},
     zbl = {1321.42038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-2-1}
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Qingying Xue. Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators. Studia Mathematica, Tome 215 (2013) pp. 97-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-2-1/