ar X iv : 0 71 0 . 29 61 v 1 [ m at h . C A ] 1 6 O ct 2 00 7 Maximal regularity and Hardy spaces
نویسنده
چکیده
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 7→ 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 1 < p, q < ∞.
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