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Norm inequalities relating one-sided singular integrals and the one-sided maximal function

Part of: Harmonic analysis in several variables Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

M. S. Riveros  and
A. de la Torre
M. S. Riveros
Affiliation:
FaMAF Universidad Nacional de Córdoba(5000) CórdobaArgentina e-mail: [email protected]
A. de la Torre
Affiliation:
Análisis Matemático Facultad de Ciencias Universidad de Málaga(29071) MálagaSpain e-mail: [email protected]
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Abstract

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In this paper we prove that if a weight w satisfies the condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal function, for 1 < p < q < ∞.

Keywords

One-sided weightsone-sided singular integrals

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42A50: Conjugate functions, conjugate series, singular integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 403 - 414
Copyright
Copyright © Australian Mathematical Society 2000

References

[AFM]Aimar, H., Forzani, L. and Reyes, F. J. Martín, ‘On weighted inequalities for one-sided singular integrals’, Proc. Amer. Math. Soc. 125 (1997), 2057–2064.CrossRefGoogle Scholar
[FeSt]Fefferman, C. and Stein, E., ‘Some maximal inequalities’, Amer. J. Math. 93 (1971), 107–115.CrossRefGoogle Scholar
[Mu]Muckenhoupt, B., ‘Norm inequalities relating the Hilbert transform to the Hardy-Littlewood maximal function’, in: Functional analysis and approximation (Oberwolfach 1980), Internat. Ser. Number. Math. 60 (Birkhauser, Basel-Boston, Mass., 1981) pp. 219–231.CrossRefGoogle Scholar
[MPT]Reyes, F. J. Martín, Pick, L. and de la Torre, A., ‘A +∞, condition’, Can. J. Math 45 (1993), 1231–1244.CrossRefGoogle Scholar
[S1]Sawyer, E., ‘Weighted inequalities for the one-sided Hardy-Littlewood maximal function’, Trans. Amer. Math. Soc. 297 (1986), 53–61.CrossRefGoogle Scholar
[S2]Sawyer, E., ‘Norm inequalities relating singular integrals and maximal functions’, Studia Math. 75 (1983), 251–263.CrossRefGoogle Scholar