Abstract
In this note we prove that (under suitable hypotheses) every homogeneous differential operator on L p( R n) N , corresponding to a system which is well-posed in L 2( R n) N , generates an α-times integrated semigroup on L p( R n) 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 ¦ .
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