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FOURIER MULTIPLIERS AND INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Published online by Cambridge University Press:  24 May 2004

VALENTIN KEYANTUO  and
CARLOS LIZAMA
VALENTIN KEYANTUO
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, University of Puerto Rico, PO Box 23355, Puerto Rico 00931, USAkeyantuo@rrpac.upr.clu.edu
CARLOS LIZAMA
Affiliation:
Departamento de Matemática, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chileclizama@usach.cl
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Abstract

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 $C^{\alpha},\,0\,{<}\, \alpha \,{<}\, 1 .$

Keywords

45N05 (primary)45D0543A1547D99 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 737 - 750
Copyright
The London Mathematical Society 2004

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