Weighted boundedness of multilinear Calderón commutators

Abstract

Abstract The main result of this paper is to give that if b ∈ Lip ⁡ ( ℝ n ) {b\in\operatorname{Lip}(\mathbb{R}^{n})} , h j ∈ BMO ⁡ ( ℝ n ) {h_{j}\in\operatorname{BMO}(\mathbb{R}^{n})} , j = 1 , … , k {j=1,\ldots,k} , k ∈ ℤ + {k\in\mathbb{Z}^{+}} and w ∈ A p {w\in A_{p}} , 1 < p < ∞ {1<p<\infty} , then the multilinear Calderón commutators T Ω , b , h → {T_{\Omega,b,\vec{h}}} with variable kernels are bounded on L p ⁢ ( w ) {L^{p}(w)} . In addition, the authors extend the above result to the Morrey space.