Variants of the Calderón-Zygmund theory for Lp-spaces.

Anthony Carbery

Revista Matemática Iberoamericana (1986)

  • Volume: 2, Issue: 4, page 381-396
  • ISSN: 0213-2230

Abstract

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The purposes of this paper may be described as follows:(i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions);(ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed?(iii) to simplify and extend the work of Duoandikoetxea and Rubio de Francia and Christ and Stein, which sometimes has unnecessarily strong assumptions, and to introduce a sensitivity to different Lp-spaces which does not appear in their work.

How to cite

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Carbery, Anthony. "Variants of the Calderón-Zygmund theory for Lp-spaces.." Revista Matemática Iberoamericana 2.4 (1986): 381-396. <http://eudml.org/doc/39335>.

@article{Carbery1986,
abstract = {The purposes of this paper may be described as follows:(i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions);(ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed?(iii) to simplify and extend the work of Duoandikoetxea and Rubio de Francia and Christ and Stein, which sometimes has unnecessarily strong assumptions, and to introduce a sensitivity to different Lp-spaces which does not appear in their work.},
author = {Carbery, Anthony},
journal = {Revista Matemática Iberoamericana},
keywords = {Operadores integrales; Espacios LP; Calderón-Zygmund theory; singular integral operator; Hörmander multiplier theorem; lacunary maximal Bochner-Riesz operator},
language = {eng},
number = {4},
pages = {381-396},
title = {Variants of the Calderón-Zygmund theory for Lp-spaces.},
url = {http://eudml.org/doc/39335},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Carbery, Anthony
TI - Variants of the Calderón-Zygmund theory for Lp-spaces.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 4
SP - 381
EP - 396
AB - The purposes of this paper may be described as follows:(i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions);(ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed?(iii) to simplify and extend the work of Duoandikoetxea and Rubio de Francia and Christ and Stein, which sometimes has unnecessarily strong assumptions, and to introduce a sensitivity to different Lp-spaces which does not appear in their work.
LA - eng
KW - Operadores integrales; Espacios LP; Calderón-Zygmund theory; singular integral operator; Hörmander multiplier theorem; lacunary maximal Bochner-Riesz operator
UR - http://eudml.org/doc/39335
ER -

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