Weighted inequalities for commutators of one-sided singular integrals

María Lorente; María Silvina Riveros

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 1, page 83-101
  • ISSN: 0010-2628

Abstract

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We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in ( - ∞ , 0 ) ) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1), 1995, pages 163–185. We improve these results for one-sided singular integrals by putting in the right hand side of the inequalities a smaller operator and a wider class of weights.

How to cite

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Lorente, María, and Riveros, María Silvina. "Weighted inequalities for commutators of one-sided singular integrals." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 83-101. <http://eudml.org/doc/249008>.

@article{Lorente2002,
abstract = {We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in $(-\infty , 0)$) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1), 1995, pages 163–185. We improve these results for one-sided singular integrals by putting in the right hand side of the inequalities a smaller operator and a wider class of weights.},
author = {Lorente, María, Riveros, María Silvina},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {one-sided weights; one-sided singular integrals; one-sided weights; one-sided singular integrals},
language = {eng},
number = {1},
pages = {83-101},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Weighted inequalities for commutators of one-sided singular integrals},
url = {http://eudml.org/doc/249008},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Lorente, María
AU - Riveros, María Silvina
TI - Weighted inequalities for commutators of one-sided singular integrals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 1
SP - 83
EP - 101
AB - We prove weighted inequalities for commutators of one-sided singular integrals (given by a Calder’on-Zygmund kernel with support in $(-\infty , 0)$) with BMO functions. We give the one-sided version of the results in C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl., vol. 3 (6), 1997, pages 743–756 and C. Pérez, Endpoint estimates for commutators of singular integral operators, J. Funct. Anal., vol 128 (1), 1995, pages 163–185. We improve these results for one-sided singular integrals by putting in the right hand side of the inequalities a smaller operator and a wider class of weights.
LA - eng
KW - one-sided weights; one-sided singular integrals; one-sided weights; one-sided singular integrals
UR - http://eudml.org/doc/249008
ER -

References

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  1. Aimar H., Forzani L., Martín-Reyes F.J., On weighted inequalities for one-sided singular integrals, Proc. Amer. Math. Soc. 125 (1997), 2057-2064. (1997) MR1376747
  2. Bennett C., Sharpley R., Interpolation of Operators, Academic Press, New York, 1988. Zbl0647.46057MR0928802
  3. Coifman R., Distribution function inequalities for singular integrals, Proc. Acad. Sci. USA 69 (1972), 2838-2839. (1972) Zbl0243.44006MR0303226
  4. Coifman R., Rochberg R., Weiss G., Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (2) (1976), 611-635. (1976) Zbl0326.32011MR0412721
  5. Martín-Reyes F.J., Pick L., de la Torre A., A ∞ + condition, Canad. J. Math. 45 (1993), 1231-1244. (1993) MR1247544
  6. Martín-Reyes F.J., de la Torre A., One sided B M O spaces, J. London Math. Soc. (2) 49 (1994), 529-542. (1994) MR1271548
  7. O'Neil R., Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc. 115 (1963), 300-328. (1963) 
  8. Pérez C., Weighted norm inequalities for singular integral operators, J. London Math. Soc. 49 (1994), 296-308. (1994) MR1260114
  9. Pérez C., Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function, J. Fourier Anal. Appl. 3 (6) (1997), 743-756. (1997) MR1481632
  10. Pérez C., Endpoint estimates for commutators of singular integral operators, J. Funct. Anal. 128 1 (1995), 163-185. (1995) MR1317714
  11. Pérez C., On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted L p -spaces with different weights, Proc. London Math. Soc. 71 (3) (1995), 135-157. (1995) MR1327936
  12. Riveros M.S., de Rosa L., de la Torre A., Sufficient conditions for one-sided operators, J. Fourier Anal. Appl 6 (6) (2000), 607-621. (2000) Zbl0984.42010MR1790246
  13. Sawyer E.T., Weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297 (1986), 53-61. (1986) Zbl0627.42009MR0849466
  14. Wilson J.M., Weighted norm inequalities for the continuous square functions, Trans. Amer. Math. Soc. 314 (1989), 661-692. (1989) Zbl0689.42016MR0972707

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