Multiparameter singular integrals and maximal functions

Fulvio Ricci; Elias M. Stein

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 3, page 637-670
  • ISSN: 0373-0956

Abstract

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We prove L p -boundedness for a class of singular integral operators and maximal operators associated with a general k -parameter family of dilations on R n . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.

How to cite

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Ricci, Fulvio, and Stein, Elias M.. "Multiparameter singular integrals and maximal functions." Annales de l'institut Fourier 42.3 (1992): 637-670. <http://eudml.org/doc/74968>.

@article{Ricci1992,
abstract = {We prove $L^ p$-boundedness for a class of singular integral operators and maximal operators associated with a general $k$-parameter family of dilations on $\{\bf R\}^ n$. This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.},
author = {Ricci, Fulvio, Stein, Elias M.},
journal = {Annales de l'institut Fourier},
keywords = {maximal functions; Calderón-Zygmund kernels; product domains; singular integral operators; maximal operators; homogeneous manifolds},
language = {eng},
number = {3},
pages = {637-670},
publisher = {Association des Annales de l'Institut Fourier},
title = {Multiparameter singular integrals and maximal functions},
url = {http://eudml.org/doc/74968},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Ricci, Fulvio
AU - Stein, Elias M.
TI - Multiparameter singular integrals and maximal functions
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 3
SP - 637
EP - 670
AB - We prove $L^ p$-boundedness for a class of singular integral operators and maximal operators associated with a general $k$-parameter family of dilations on ${\bf R}^ n$. This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.
LA - eng
KW - maximal functions; Calderón-Zygmund kernels; product domains; singular integral operators; maximal operators; homogeneous manifolds
UR - http://eudml.org/doc/74968
ER -

References

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