Título inglés |
On the product theory of singular integrals. |
Título español |
Sobre la teoría de integrales singulares producto. |
Autor/es |
Nagel, Alexander ; Stein, Elias M. |
Organización |
Dep. Math. Univ. Wisconsin, Madison (Wisconsin), Estados Unidos; Dep. Math. Princeton Univ. Princeton (New Jersey), Estados Unidos |
Revista |
0213-2230 |
Publicación |
2004, 20(2): 531-561, 15 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
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. |
Clasificación UNESCO |
120213 |
Palabras clave español |
Integrales singulares ; Operadores acotados ; Littlewood-Paley |
Código MathReviews |
MR2073131 |
Código Z-Math |
Zbl 1057.42016 |
Acceso al artículo completo |