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

• Autorzy: Qingying Xue
• Języki publikacji: EN

Abstrakty

EN

The following iterated commutators $T_{∗,Πb}$ of the maximal operator for multilinear singular integral operators and $I_{α,Πb}$ of the multilinear fractional integral operator are introduced and studied:
$T_{∗,Πb}(f⃗)(x) = sup_{δ>0} |[b₁,[b₂,…[b_{m-1},[bₘ,T_{δ}]ₘ]_{m-1} ⋯]₂]₁ (f⃗)(x)|$,
$I_{α,Πb}(f⃗)(x) = [b₁,[b₂,…[b_{m-1},[bₘ,I_{α}]ₘ]_{m-1}⋯]₂]₁(f⃗)(x)$,
where $T_{δ}$ are the smooth truncations of the multilinear singular integral operators and $I_{α}$ is the multilinear fractional integral operator, $b_{i} ∈ BMO$ 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, $A_{p⃗}$ and $A_{(p⃗,q)}$, are obtained, respectively.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 217
• Numer: 2
• Strony: 97-122

Daty

wydano

2013

Twórcy

autor

Qingying Xue

• School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P.R. China

Identyfikatory

DOI

10.4064/sm217-2-1