Original research
Some estimates for multilinear commutators on the weighted Morrey spaces
Department of Mathematics and Information Sciences, East China Jiao Tong University, Nanchang Jiangxi, 330013, People’s Republic of China
Mathematical Sciences 2012, 6:33 doi:10.1186/2251-7456-6-33
Published: 5 September 2012Abstract
Purpose
The purpose of this paper is to study the multilinear commutator in weighted Morrey space.
Methods
We divide the multilinear commutator into four parts and apply with the methods of weighted Lebesgue space and Pérez and Trujillo-González.
Results
Let
; we show that
is bounded on weighted Morrey spaces Lp,κ(w),1 < p < ∞,0 < κ < 1,w ∈ Ap. When p = 1, it is shown that
is weak type bounded on weighted Morrey space.
Conclusions
We extend the results of the commutator in weighted Morrey space. In particular, for m=1, this result is also new in the classical commutator.
