Estimates for maximal singular integrals

Loukas Grafakos

Colloquium Mathematicae (2003)

  • Volume: 96, Issue: 2, page 167-177
  • ISSN: 0010-1354

Abstract

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It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and L p -bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.

How to cite

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Loukas Grafakos. "Estimates for maximal singular integrals." Colloquium Mathematicae 96.2 (2003): 167-177. <http://eudml.org/doc/285118>.

@article{LoukasGrafakos2003,
abstract = {It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and $L^\{p\}$-bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.},
author = {Loukas Grafakos},
journal = {Colloquium Mathematicae},
keywords = {singular integral; maximal singular integral; Calderón-Zygmund theory},
language = {eng},
number = {2},
pages = {167-177},
title = {Estimates for maximal singular integrals},
url = {http://eudml.org/doc/285118},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Loukas Grafakos
TI - Estimates for maximal singular integrals
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 2
SP - 167
EP - 177
AB - It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and $L^{p}$-bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.
LA - eng
KW - singular integral; maximal singular integral; Calderón-Zygmund theory
UR - http://eudml.org/doc/285118
ER -

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