Bilinear Multipliers on Banach Function Spaces
Author
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-03-03
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Let X 1 , X 2 , X 3 be Banach spaces of measurable functions in L 0 ( R ) and let m ( ξ , η ) be a locally integrable function in R 2 .
We say that m ∈ B M ( X 1 , X 2 , X 3 ) ( R ) if B m ( f , g ) ( x ) = ∫ R ∫ R f ^ ( ξ ) g ^ ( η ) m ( ξ , η ) e 2 π i < ξ + η , x > d ξ d η , defined for f and g with compactly supported Fourier transform, extends to a bounded bilinear operator from X 1 × X 2 to X 3 .
In this paper we investigate some properties of the class B M ( X 1 , X 2 , X 3 ) ( R ) for general spaces which are invariant under translation, modulation, and dilation, analyzing also the particular case of r.i.
Banach function spaces.
We shall give some examples in this class and some procedures to generate new bilinear multipliers.
We shall focus on the case m ( ξ , η ) = M ( ξ - η ) and find conditions for these classes to contain nonzero multipliers in terms of the Boyd indices for the spaces.
American Psychological Association (APA)
Blasco, Oscar. 2019. Bilinear Multipliers on Banach Function Spaces. Journal of Function Spaces،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1174910
Modern Language Association (MLA)
Blasco, Oscar. Bilinear Multipliers on Banach Function Spaces. Journal of Function Spaces No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1174910
American Medical Association (AMA)
Blasco, Oscar. Bilinear Multipliers on Banach Function Spaces. Journal of Function Spaces. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1174910
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174910