An explicit counterexample for the Lp-maximal regularity problem

In this short Note we give a self-contained example of a consistent family of holomorphic semigroups (T-p(t))(t >= 0) such that (T-p(t))(t >= 0) does not have maximal regularity for p > 2. This answers negatively the open question whether maximal regularity extrapolates from L-2 to the L-p-scale. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.