$b$-coercive convolution equations in weighted function spaces and applications

  • H. K. Musaev
  • V. B. Shakhmurov

Abstract

We study the $b$-separability properties of 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 of the Cauchy problem for a parabolic convolution equation are established. Finally, these results are applied to obtain the maximal regularity properties for anisotropic integro-differential equations and the system of infinitely many convolution equations.
Published
25.10.2017
How to Cite
MusaevH. K., and ShakhmurovV. B. “$b$-Coercive Convolution Equations in Weighted Function spaces and Applications”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 10, Oct. 2017, pp. 1385-0, http://umj.imath.kiev.ua/index.php/umj/article/view/1789.
Section
Research articles