Fourier Multipliers and Integro‐Differential Equations in Banach Spaces

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Hölder continuous solutions for fractional differential equations and maximal regularity (2013, unknown): “7 have been obtained [11, 28].”
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.”
Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces (2005, methodology): “Our results use, on the one hand, recent papers by Arendt–Bu [5], [6], Arendt–Batty–Bu [3] where the above problem is studied with a(·) ≡ 0, b(·) ≡ 0 and, on the other hand, Keyantuo–Lizama [20] where the problem (1.”
lp ‐maximal regularity for fractional difference equations on UMD spaces (2015, methodology): “We observe that maximal regularity for evolution equations using methods of operator valued Fourier multiplier theorems has been studied intensively in the last two decades; see [3], [22], [36] and references therein.”
Fourier multipliers and periodic solutions of delay equations in Banach spaces (2006, methodology): “On the other hand, various connections of periodicity for differential equations and Fourier multipliers were recently noticed in the work by Arendt-Bu [3] and [13, 14].”