On maximal Lp-regularity

The aim of this paper is to propose weak assumptions to prove maximal Lq regularity for Cauchy problem: du dt (t) −Lu(t) = f (t). Mainly we only require “off-diagonal” estimates on the real semigroup (etL)t>0 to obtain maximal Lq regularity. The main idea is to use one kind of Hardy space H1 adapted to this problem and then use interpolation results. These techniques permit us to prove weighted maximal regularity too. © 2009 Elsevier Inc. All rights reserved