B-Coercive Convolution Equations in Weighted Function Spaces and Their Applications

Abstract

We study the properties of B-separability for elliptic convolution operators in weighted Besov spaces and establish sharp estimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, in addition, play the role of negative generators of analytic semigroups. Moreover, the maximal B-regularity properties are established for the Cauchy problem for a parabolic convolution equation. Finally, these results are applied to obtain the maximal regularity properties for anisotropic integrodifferential equations and a system of infinitely many convolution equations.