Maximal regularity and Hardy spaces

الأصل · EN

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 Lq regularity on Lᵖ spaces for p,q between 1 and ∞.