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Weights for commutators of the one-sided discrete square function, the Weyl fractional integral and other one-sided operators

Published online by Cambridge University Press:  12 July 2007

M. Lorente  and
M. S. Riveros
M. Lorente
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus Teatinos 29071 Málaga, Spain(lorente@anamat.cie.uma.es)
M. S. Riveros
Affiliation:
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM–Conicet, 5000 Córdoba, Argentina(sriveros@mate.uncor.edu)
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Abstract

The purpose of this paper is to prove strong-type inequalities with one-sided weights for commutators (with symbol b ∈ BMO) of several one-sided operators, such as the one-sided discrete square function, the one-sided fractional operators, or one-sided maximal operators given by the convolution with a smooth function. We also prove that b ∈ BMO is a necessary condition for the boundedness of commutators of these one-sided operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 4 , August 2005 , pp. 845 - 862
Copyright
Copyright © Royal Society of Edinburgh 2005

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