Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-29T02:12:12.463Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Aimar, H., Forzani, L. and Martín-Reyes, F. J., ‘On weighted inequalities for one-sided singular integrals’, Proc. Amer. Math. Soc. 125 (1997), 2057–2064.CrossRefGoogle Scholar
[2]Bloom, S., ‘A commutator theorem and weighted BMO’, Trans. Amer. Math. Soc. 292 (1985), 103–122.CrossRefGoogle Scholar
[3]Coifman, R. R. and Fefferman, C., ‘Weighted norm inequalities for maximal functions and singular integrals’, Studia Math. 51 (1974), 241–250.CrossRefGoogle Scholar
[4]Lorente, M. and Riveros, M. S., ‘Weighted inequalities for commutators of one-sided singular integrals’, Comment. Math. Univ. Carolin. 43 (2002), 83–101.Google Scholar
[5]Martín-Reyes, F. J., ‘New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions’, Proc. Amer. Math. Soc. 117 (1993), 691–698.Google Scholar
[6]Martín-Reyes, F. J. and de la Torre, A., ‘One sided BMO spaces’, J. London Math. Soc. 49 (1994), 529–542.CrossRefGoogle Scholar
[7]Martín-Reyes, F. J., Ortega, P. and de la Torre, A., ‘Weighted inequalities for one sided maximal functions’, Trans. Amer. Math. Soc. 319 (1990), 517–534.CrossRefGoogle Scholar
[8]Martín-Reyes, F. J., Pick, L. and de la Torre, A., ‘A+∞ condition’, Canad. J. Math. 45 (1993), 1231–1244.CrossRefGoogle Scholar
[9]Muckenhoupt, B., ‘Weighted norm inequalities for the Hardy maximal function’, Trans. Amer. Math. Soc. 165 (1972), 207–226.CrossRefGoogle Scholar
[10]Riveros, M. S. and de la Torre, A., ‘Norm inequalities relating one-sided singular integrals and the one-sided maximal function’, J. Austral. Math. Soc.(Series A) 69 (2000), 403–414.CrossRefGoogle Scholar
[11]Riveros, M. S. and de la Torre, A., ‘On the best ranges for A+p and RH+r’, Czechoslovak Math. J. 51 (2001), 285–301.CrossRefGoogle Scholar
[12]Sawyer, E. T., ‘Weighted inequalities for the one-sided Hardy-Littlewood maximal functions’, Trans. Amer. Math. Soc. 297 (1986), 53–61.CrossRefGoogle Scholar
[13]Segovia, C. and Torrea, J. L., ‘Vector-valued commutators and applications’, Indiana Univ. Math. J. 38 (1989), 959–971.CrossRefGoogle Scholar
[14]Strömberg, J. and Torchinsky, A., Weighted Hardy spaces, Lecture Notes in Math. 1381 (Springer, Berlin, 1989).Google Scholar
[15]de la Torre, A. and Torrea, J. L., ‘One-sided discrete square function’, Studia Math. 156 (2003), 243–260.CrossRefGoogle Scholar