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Calderón reproducing formulas and applications to Hardy spaces

  • Pascal Auscher [3] ; Alan G.R. McIntosh [1] ; Andrew J. Morris [2]
    1. [1] Australian National University

      Australian National University

      Australia

    2. [2] University of Oxford

      University of Oxford

      Oxford District, Reino Unido

    3. [3] Université de Paris-Sud
  • Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 3, 2015, págs. 865-900
  • Idioma: inglés
  • DOI: 10.4171/RMI/857
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • We establish new Calderón holomorphic functional calculus whilst the synthesising function interacts with D through functional calculus based on the Fourier transform. We apply these to prove the embedding HpD(∧T∗M)⊆Lp(∧T∗M), 1≤p≤2, for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ, where D=d+d∗ is the Hodge–Dirac operator on a complete Riemannian manifold M that has doubling volume growth. This fills a gap in that work. The new reproducing formulas also allow us to obtain an atomic characterisation of H1D(∧T∗M). The embedding HpL⊆Lp, 1≤p≤2, where L is either a divergence form elliptic operator on Rn, or a nonnegative self-adjoint operator that satisfies Davies–Gaffney estimates on a doubling metric measure space, is also established in the case when the semigroup generated by the adjoint −L∗ is ultracontractive.


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