$b$-coercive convolution equations in weighted function spaces and applications - Musaev, H. K.; Shakhmurov, V. B. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We study the $b$-separability properties of elliptic convolution operators in weighted Besov spaces and establish sharpestimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, inaddition, play the role of negative generators of analytic semigroups. Moreover, the maximal $b$-regularity properties ofthe Cauchy problem for a parabolic convolution equation are established. Finally, these results are applied to obtain themaximal regularity properties for anisotropic integro-differential equations and the system of infinitely many convolutionequations.