Compactness for the Commutator of the Multilinear Fourier Multiplier on the Morrey Space

Given s1,…, sm ∈ (n/2, n], let Tσ be a multilinear Fourier multiplier operator associated with a multilinear multiplier σ satisfying a Sobolev regularity condition supℓ∈ℤ∥σℓ∥Ws1,…,sm(ℝmn)<∞. By the strongly precompactness of Banach space, the authors prove that if b1, … , bm∈ CMO(ℝn) , then the commutator Tσ,Σb is a compact operator from the product Morrey space Lp1,λ(ℝn)×⋯×Lpm,λ(ℝn) to the Morrey space Lp , λ(ℝn). As an application, the compactness of the commutator Tσ,Σb from the product Morrey space Lp1,λ(ℝn)×⋯×Lpm,λ(ℝn) to the Morrey space Lp , λ(ℝn) is also obtained under the Sobolev regularity condition supℓ∈ℤ∥σℓ∥Ws(ℝmn)<∞ for s∈(mn/2, mn]. © 2015, Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.