OPERATOR-VALUED FOURIER MULTIPLIERS ON PERIODIC BESOV SPACES AND APPLICATIONS

By Wolfgang Arendt, Shangquan Bu. Proceedings of the Edinburgh Mathematical Society, 2004

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Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “For more on vector-valued Besov spaces, we refer to Arendt Batty and Bu [7].”
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, background): “Note that almost all publications concern only the case of R, but the periodic theory is parallel (see, for instance, [24, 70]; see also [3] for the vector-valued case).”
Periodic solutions of degenerate differential equations in vector-valued function spaces (2011, background): “For the definition and main properties of these spaces we refer to [4] or [22].”
Fourier Multipliers and Integro‐Differential Equations in Banach Spaces (2004, methodology): “In this section, we use the results of [5] to characterize maximal regularity of equation (1.”
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, background): “We note that periodic vector-valued Besov spaces were only introduced recently (see the paper [4] where Fourier multipliers in this context are studied for the first time), in contrast with periodic Hölder spaces which has been previously used in the literature.”
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation (2016, methodology): “The solutions with wave speed μ ∈ [1, 2] are in one-to-one-correspondence with the former via the Galilean transformation (6.”