Abstract

BARRAZA MARTINEZ, Bienvenido; GONZALEZ MARTINEZ, Iván  and  HERNANDEZ MONZON, Jairo. Operator-valued Fourier multipliers on toroidal Besov spaces. Rev.colomb.mat. [online]. 2016, vol.50, n.1, pp.109-137. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v50n1.62205.

Abstract We prove in this paper that a sequence M: Zⁿ → L(E) of bounded variation is a Fourier multiplier on the Besov space B^s_{p, q}(Tⁿ, E) for s ∈ R, 1 < p < ∞, 1 ≤ q ≤ 1 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.

Keywords : Fourier multipliers; operator-valued symbols; UMD-spaces; toroidal Besov spaces.

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