On the product theory of singular integrals.

Alexander Nagel; Elias M. Stein

Revista Matemática Iberoamericana (2004)

  • Volume: 20, Issue: 2, page 531-561
  • ISSN: 0213-2230

Abstract

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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.

How to cite

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Nagel, Alexander, and Stein, Elias M.. "On the product theory of singular integrals.." Revista Matemática Iberoamericana 20.2 (2004): 531-561. <http://eudml.org/doc/39722>.

@article{Nagel2004,
abstract = {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.},
author = {Nagel, Alexander, Stein, Elias M.},
journal = {Revista Matemática Iberoamericana},
keywords = {Integrales singulares; Operadores acotados; Littlewood-Paley; product space; singular integral; Littlewood-Paley theory; heat kernel; sub-Laplacian},
language = {eng},
number = {2},
pages = {531-561},
title = {On the product theory of singular integrals.},
url = {http://eudml.org/doc/39722},
volume = {20},
year = {2004},
}

TY - JOUR
AU - Nagel, Alexander
AU - Stein, Elias M.
TI - On the product theory of singular integrals.
JO - Revista Matemática Iberoamericana
PY - 2004
VL - 20
IS - 2
SP - 531
EP - 561
AB - 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.
LA - eng
KW - Integrales singulares; Operadores acotados; Littlewood-Paley; product space; singular integral; Littlewood-Paley theory; heat kernel; sub-Laplacian
UR - http://eudml.org/doc/39722
ER -

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