Operator-valued Fourier multipliers on toroidal Besov spaces
We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the a...
- Autores:
-
Barraza Martínez, Bienvenido
González Martínez, Iván
Hernández Monzón, Jairo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66457
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66457
http://bdigital.unal.edu.co/67485/
- Palabra clave:
- 51 Matemáticas / Mathematics
Fourier multipliers
operator-valued symbols
UMD- spaces
toroidal Besov spaces
Multiplicadores de Fourier
símbolos operador-valuados
espacios UMD
espacios de Besov toroidales.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | We prove in this paper that a sequence M: Zn → L(E) of bounded variation is a Fourier multiplier on the Besov space Bsp, q(Tn, E) for s ∈ R, 1 p ∞, 1 ≤ q ≤ ∞ and E a Banach space, if and only if E is a UMD-space. This extends the Theorem 4.2 in [3] to the n-dimensional case. As illustration of the applicability of this results we study the solvability of two abstract Cauchy problems with periodic boundary conditions. |
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