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...

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Detalles Bibliográficos
Autores: Barraza Martínez, Bienvenido, González Martínez, Iván, Hernández Monzón, Jairo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Colombia
Institución:Universidad Nacional de Colombia
Repositorio:Repositorio UN
Idioma:español
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/
Access Level:acceso abierto
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.
Descripción
Sumario: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.