Functional calculus for first order systems of Dirac type and boundary value problems. II: \(L^p\)-\(L^q\) theory for holomorphic functions of perturbed first order Dirac operators (Q2801548)

The main contribution of this work consists of some \(L^p\)-\(L^q\) estimates for some classes of Dirac first order systems. In the first part, the author establishes sufficient conditions for \(L^p\)-\(L^q\) off-diagonal estimates and \(L^p\)-\(L^q\) boundedness for operators in the functional calculus of perturbed first order Dirac operators. This is performed in terms of decay properties at 0 and \(\infty\) for the associated holomorphic functions. Next, the author discusses some conditions when the range of the perturbed first order Dirac operator is stable under multiplication by smooth cut-off functions. The final sections of the paper under review deals with a necessary condition for the \(L^p\)-\(L^q\) boundedness when \(p<q\) and some analytic extensions of the results to complex times \(t\).NEWLINENEWLINEFor Part I of this paper see [Zbl 1346.35048].