Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-29
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let T σ be the multilinear Fourier multiplier operator associated with multiplier σ satisfying the Sobolev regularity that s u p l ∈ Z σ l W s 1 , … , s m ( R m n ) < ∞ for some s k ∈ ( n / 2 , n ] ( k = 1 , … , m ) .
The authors prove that if b 1 , … , b m ∈ B M O ( R n ) and w ⃗ ∈ ∏ k = 1 m A p k / t k ( t k = n / s k ) , then the commutator T σ , Σ b is bounded from L p 1 ( R n , w 1 ) × ⋯ × L p m ( R n , w m ) to L p ( R n , ν w ⃗ ) .
Moreover, the authors also prove that if b 1 , … , b m ∈ V M O ( R n ) and w ⃗ ∈ ∏ k = 1 m A p k / t k ( t k = n / s k ) , then the commutator T σ , Σ b is compact operator from L p 1 ( R n , w 1 ) × ⋯ × L p m ( R n , w m ) to L p ( R n , ν w ⃗ ) .
American Psychological Association (APA)
Jiang, Zhou& Li, Peng. 2014. Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space. Journal of Function Spaces،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1040690
Modern Language Association (MLA)
Jiang, Zhou& Li, Peng. Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space. Journal of Function Spaces No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1040690
American Medical Association (AMA)
Jiang, Zhou& Li, Peng. Compactness of the Commutator of Multilinear Fourier Multiplier Operator on Weighted Lebesgue Space. Journal of Function Spaces. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1040690
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1040690