On maximal L~p-regularity

摘要

The aim of this paper is to propose weak assumptions to prove maximal L~q regularity for Cauchy problem: du dt(t)—Lu(t)=f(t). Mainly we only require "off-diagonal" estimates on the real semigroup (e~(tL))_t>0 to obtain maximal L~q regularity. The main idea is to use one kind of Hardy space H~1 adapted to this problem and then use interpolation results. These techniques permit us to prove weighted maximal regularity too.