Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2013 | 217 | 2 | 97-122

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

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.

97-122

wydano
2013

### Twórcy

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