On the inverse of the sum of two sectorial operators

Abstract

We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^{\infty }$-calculus is sufficient for maximal regularity of the solution. We apply the result to the abstract parabolic problem, to give a maximal $L^p$-regularity condition. We also study the abstract hyperbolic problem and give a sufficient condition for the existence of solution.

arXiv comment10 pages