On Maximal L^p-regularity

Frédéric Bernicot (1) , Jiman Zhao (2, 3)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Capital Normal University [Beijing]
3 Department of Computer Science and Engineering

The aim of this paper is to propose weak assumptions to prove maximal L^q regularity for Cauchy problem~: du/dt - 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 a 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.

Mots clés: Maximal regularity; Hardy spaces; atomic decomposition

Domaines: Analyse classique [math.CA]

Frédéric Bernicot, Jiman Zhao. On Maximal L^p-regularity. Journal of Functional Analysis, 2009, 256 (8), pp.2561-2586. ⟨hal-00361474⟩