Fourier multipliers for Holder continuous functions and maximal regularity

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Fourier Multipliers and Integro‐Differential Equations in Banach Spaces (2004, methodology): “For more details, we refer to Arendt and Bu [3, 4].”
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, background): “9 in various situations by use of the operator-valued multiplier theorems established in [5], [3], [6].”
Periodic solutions of second order differential equations in Banach spaces (2006, methodology): “To achieve our goals, we make extensive use of recent results from the papers Arendt-Bu [6], [5] and Keyantuo-Lizama [25], and the methods are based on operatorvalued Fourier multipliers theorems.”
lp ‐maximal regularity for fractional difference equations on UMD spaces (2015, methodology): “For instance, on the real line, it has been treated by means of the Amann-Weiss multiplier theorem [4], [42] and on compact intervals by use of the Arendt-Bu multiplier theorem [6], [7].”
Hölder continuous solutions for fractional differential equations and maximal regularity (2013, methodology): “In [4], Arendt, Batty and Bu study the existence and uniqueness of Hölder continuous solutions to equation (1.”