On maximal \(L^p\)-regularity (Q1017690)

The main goal of this paper is to prove maximal \(L^p\)-regularity for a Cauchy problem under the weakest possible conditions. The authors improve a result of \textit{S.\,Blunck} and \textit{P.\,C.\thinspace Kunstmann} [Adv.\ Differ.\ Equ.\ 7, No.\,12, 1513--1532 (2002; Zbl 1045.34031)], where maximal regularity was proved using weaker assumptions (with respect to classical papers on this subject) associated to ``off-diagonal'' estimates on the semigroup. The authors first prove the boundedness of the operator of maximal regularity and its adjoint on appropriate Hardy spaces. Then their main result follows by using interpolation theory and previous results proved by the authors.