Maximal regularity and Hardy spaces

• Autores: Pascal Auscher, Frédéric Bernicot, Jiman Zhao
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 59, Fasc. 1, 2008, págs. 103-127
• Idioma: inglés
• DOI: 10.1007/bf03191184
• Enlaces
  • Texto completo
• Resumen

  • 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 $1 ? p, q ? \infty$.

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