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

Qingying Xue. "Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators." Studia Mathematica 217.2 (2013): 97-122. <http://eudml.org/doc/285816>.

@article{QingyingXue2013,
abstract = {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.},
author = {Qingying Xue},
journal = {Studia Mathematica},
keywords = {multilinear maximal operators; fractional integral operators; weighted estimates; iterated commutators},
language = {eng},
number = {2},
pages = {97-122},
title = {Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators},
url = {http://eudml.org/doc/285816},
volume = {217},
year = {2013},
}

TY - JOUR
AU - Qingying Xue
TI - Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators
JO - Studia Mathematica
PY - 2013
VL - 217
IS - 2
SP - 97
EP - 122
AB - 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.
LA - eng
KW - multilinear maximal operators; fractional integral operators; weighted estimates; iterated commutators
UR - http://eudml.org/doc/285816
ER -