An explicit counterexample for the \(L^p\)-maximal regularity problem (Q1942078)

In this note, the author gives a very interesting self-contained example of a consistent family of holomorphic semigroups \((T_{p}(t))_{t\geqslant 0}\) such that \((T_{p}(t))_{t\geqslant 0}\) does not have maximal regularity for \(p>2\). It is known that holomorphy is a property that extrapolates from \(L^2\) to \(L^p\) and one can conjecture that the same happens for maximal regularity. This explicit counterexample says that the answer to this question is negative.