FOURIER MULTIPLIERS AND INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

VALENTIN KEYANTUO; CARLOS LIZAMA

doi:10.1112/S0024610704005198

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

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FOURIER MULTIPLIERS AND INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

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FOURIER MULTIPLIERS AND INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

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