Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space. (29th May 2014)

• Record Type: Journal Article
• Authors: Zhou, Jiang; Li, Peng
• Other Names: Fu Yongqiang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-05-29
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/606504
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : LetT σ be the multilinear Fourier multiplier operator associated with multiplierσ satisfying the Sobolev regularity thats u p l ∈ Z σ l W s 1, …, s m ( R m n ) < ∞ for somes k ∈ ( n / 2, n ] ( k = 1, …, m ) . The authors prove that ifb 1, …, b m ∈ B M O ( R n ) andw ⃗ ∈ ∏ k = 1 m ‍ A p k / t k ( t k = n / s k ), then the commutatorT σ, Σ b is bounded fromL p 1 ( R n, w 1 ) × ⋯ × L p m ( R n, w m ) toL p ( R n, ν w ⃗ ) . Moreover, the authors also prove that ifb 1, …, b m ∈ V M O ( R n ) andw ⃗ ∈ ∏ k = 1 m ‍ A p k / t k ( t k = n / s k ), then the commutatorT σ, Σ b is compact operator fromL p 1 ( R n, w 1 ) × ⋯ × L p m ( R n, w m ) toL p ( R n, ν w ⃗ ) .