Maximal regularity and Hardy spaces

Details Maximal regularity and Hardy spaces Maximal regularity and Hardy spaces

2007-10-16

arxiv.org/abs/0710.2961v1

Mathematics

Classical Analysis and ODEs

27 pages

Scientific paper

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 $f\mapsto Au$ 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 $\infty$.

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