On the admissibility of observation operators for evolution families (Q2163875)

In the paper under review, the author considers the unbounded observation operators for non-autonomous evolution equations of first order. The corresponding operator family \((A(t))_{t\in [0,\tau]}\) under the consideration of the author satisfies the relative \(p\)-Dini condition and each single operator \(A(t)\) has maximal regularity. Under these assumptions, there exists an evolution system associated with the family \((A(t))_{t\in [0,\tau]}\). The main results of paper are obtained by assuming that the operator family \((A(t))_{t\in [0,\tau]}\) is Hölder continuous or Lipschitz continuous.