On the product theory of singular integrals

• Autores: A. Nagel, Elias M. Stein
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 20, Nº 2, 2004, págs. 531-562
• Idioma: inglés
• DOI: 10.4171/rmi/400
• Títulos paralelos:
  • Sobre la teoría de integrales singulares producto.
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• Resumen

  • We establish Lp-boundedness for a class of product singular integral operators on spaces M = M1 x M2 x . . . x Mn. Each factor space Mi is a smooth manifold on which the basic geometry is given by a control, or Carnot-Carathéodory, metric induced by a collection of vector fields of finite type. The standard singular integrals on Mi are non-isotropic smoothing operators of order zero. The boundedness of the product operators is then a consequence of a natural Littlewood- Paley theory on M. This in turn is a consequence of a corresponding theory on each factor space. The square function for this theory is constructed from the heat kernel for the sub-Laplacian on each factor.