Operator-valued Fourier multipliers on toroidal Besov spaces

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 illustratio...

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Veröffentlicht in:Revista colombiana de matemáticas 2016-01, Vol.50 (1), p.109-137
Hauptverfasser: Barraza Martínez, Bienvenido, González Martínez, Iván, Hernández Monzón, Jairo
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Boundary conditions
Fourier analysis
Fourier transforms
Function space
MATHEMATICS
Multipliers
Theoretical mathematics
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Zusammenfassung: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.
ISSN:0034-7426
2357-4100
DOI:10.15446/recolma.v50n1.62205