Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces

Shangquan Bu, Yi Fang
2008 Studia Mathematica  
We study the maximal regularity on different function spaces of the second order integro-differential equations with infinite delay where A is a closed operator in a Banach space X, α ∈ C, and a, b ∈ L 1 (R + ). We use Fourier multipliers to characterize maximal regularity for (P ). Using known results on Fourier multipliers, we find suitable conditions on the kernels a and b under which necessary and sufficient conditions are given for the problem (P ) to have maximal regularity on L p (T, X),
more » ... rity on L p (T, X), periodic Besov spaces B s p,q (T, X) and periodic Triebel-Lizorkin spaces F s p,q (T, X). 2000 Mathematics Subject Classification: Primary 45N05; Secondary 45D05, 43A15, 47D99.
doi:10.4064/sm184-2-1 fatcat:5svljbfgrrgvph3eal4wk6cavu