Services on Demand
Journal
Article
Indicators
Cited by SciELO
Access statistics
Related links
Cited by Google
Similars in SciELO
Similars in Google
Share
Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
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 Bsp, 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.