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Two weight norm inequalities for communtators of one-sided singular integrals and the one-sided discrete square function

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

M. Lorente  and
M. S. Riveros
M. Lorente
Affiliation:
Análisis MatemáticoFacultad de CienciasUniversided de Málaga29071 MálagaSpain e-mail: lorente@anamat.cie.uma.es
M. S. Riveros
Affiliation:
FaMAFUniversidad Nacional de CórdobaCIEM (CONICET)5000 CórdobaArgentina e-mail: sriveros@mate.uncor.edu
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Abstract

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The purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (-∞, 0)) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.

Keywords

one-sided weightsone-sided singular integrals.

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 77 - 94
Copyright
Copyright © Australian Mathematical Society 2005

References

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