Maximal regularity and Hardy spaces

2007/10/16 by Auscher, Pascal, Bernicot, Frédéric, Zhao, Jiman · 1 citation
#34G10 #35K90 #42B20 #42B30 #47D06 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0710.2961

Abstract

In this work, we consider the Cauchy problem for u' - Au = f with A the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity f↦ Au and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain the maximal L^q regularity on L^p spaces for p,q between 1 and ∞.

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