Maximal Regular Convolution-Differential Equations in Weighted Besov Spaces

Abstract

By using Fourier multiplier theorems, the maximal regularity properties of abstract convolution differential equations in weighted Besov spaces are investigated. It is shown that the corresponding convolution differential operators are positive and generate analytic semi groups in abstract Besov spaces. Then, the well-posedness of the Cauchy problem for parabolic convolution operator equation is established. Moreover, these results are used to establish maximal regularity properties for system of integro-differential equations of finite and infinite orders.