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Journal of the London Mathematical Society 2004 69(3):737-750; doi:10.1112/S0024610704005198
© 2004 by London Mathematical Society
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© The London Mathematical Society

Fourier Multipliers and Integro-Differential Equations in Banach Spaces

Valentin Keyantuo and Carlos Lizama

Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico PO Box 23355, Puerto Rico 00931, USA, keyantuo{at}rrpac.upr.clu.edu
Departamento de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile Casilla 307-Correo 2, Santiago, Chile, clizama{at}usach.cl

Received 15 February 2003. Revision received 21 October 2003.

Operator-valued Fourier multiplier theorems are used to establish maximal regularity results for an integro-differential equation with infinite delay in Banach spaces. Results are obtained under general conditions for periodic solutions in the vector-valued Lebesgue and Besov spaces. The latter scale includes in particular the Hölder spaces C{alpha}, 0 < {alpha} < 1 .


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