Integrated semigroups and the cauchy problem for systems in L^p spaces

In this note we prove that (under suitable hypotheses) every homogeneous differential operator on L^p(Rⁿ)^N, corresponding to a system which is well-posed in L²(Rⁿ)^N, generates an α-times integrated semigroup on L^p(Rⁿ)^N (1 <p <∞) whenever α > n | 1 2 - 1 p|. For some special systems of mathematical physics, such as the wave equation or Maxwell's equations this constant can be improved to be (n - 1) | 1 2 - 1 p|.