Journal of Fourier Analysis and Applications

, Volume 3, Issue 6, pp 743–756

Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function

  • Carlos Pérez


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Chang, S.Y.A., Wilson, J.M., and Wolff, T.H. (1985). Some weighted norm inequalities concerning the Schrödinger operators.Comm. Math. Helvetici 60, 217–286.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Chiarenza, F., Frasca, M., and Longo, P. (1991). InteriorW 2,p estimates for non divergence elliptic equations with discontinuous coefficients.Ricerche Mat. 40, 149–168.MATHMathSciNetGoogle Scholar
  3. [3]
    Chiarenza, F., Frasca, M., and Longo, P. (1993).W 2,p- solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients.Trans. Amer. Math. Soc. 334, 841–853.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Coifman, R. (1972). Distribution function inequalities for singular integrals.Proc. Acad. Sci. U.S.A. 69, 2838–2839.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Coifman, R., Rochberg, R., and Weiss, G. (1976). Factorization theorems for Hardy spaces in several variables.Ann. of Math.(2)103, 611–635.CrossRefMathSciNetGoogle Scholar
  6. [6]
    Di Fazio, G. and Ragusa, M.A. (1993). Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients.J. Funct. Anal. 112, 241–256.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Garcia-Cuerva, J. and Rubio de Francia, J.L. (1985). Weighted norm inequalities and related topics.North-Holland Math. Stud. 116. North-Holland, Amsterdam.Google Scholar
  8. [8]
    Greco, L. and Iwaniec, T. (1994). New inequalities for the Jacobian.Ann. Inst. H. Poincare 11, 17–35.MATHMathSciNetGoogle Scholar
  9. [9]
    Hunt, R.A., Muckenhoupt, B., and Wheeden, R.L. (1973). Weighted norm inequalities for the conjugate function and Hilbert transform.Trans. Amer. Math. Soc. 176, 227–252.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Iwaniec, T. and Sbordone, C. Weak minima of variational integrals.J. Reine Angew Math. 454, 143–161.Google Scholar
  11. [11]
    Janson, S. (1978). Mean oscillation and commutators of singular integral operators.Ark. Math. 16, 263–270.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Journé, J.L. (1983). Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón.Lecture Notes in Math. 994. Springer-Verlag, New York.Google Scholar
  13. [13]
    Milman, M. (1995). Extrapolation and optimal decompositions.Lecture Notes in Math. 1580. Springer-Verlag, New York.Google Scholar
  14. [14]
    O’Neil, R. (1963). Fractional integration in Orlicz spaces.Trans. Amer. Math. Soc. 115, 300–328.CrossRefMathSciNetGoogle Scholar
  15. [15]
    O’Neil, R. (1968). Integral transforms and tensor products on Orlicz spaces andL p,q spaces.J. Anal. Math. 21, 1–276.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Pérez, C. (1995). On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weightedL p -spaces with different weights.Proc. London Math. Soc. (3)71, 135–157.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    Pérez, C. (1995). Endpoint estimates for commutators of singular integral operators.J. Funct. Anal. 128, 163–185.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Pérez, C. (1994). Weighted norm inequalities for singular integral operators.J. London Math. Soc. 49, 296–308.MATHMathSciNetGoogle Scholar
  19. [19]
    Rochberg, R. and Weiss, G. (1983). Derivatives of analytic families of Banach spaces.Ann. of Math. (2)118.Google Scholar
  20. [20]
    Stein, E.M. (1969). Note on the classL logL.Studia Math. 32, 305–310.MATHMathSciNetGoogle Scholar
  21. [21]
    Wilson, J.M. (1989). Weighted norm inequalities for the continuos square functions.Trans. Amer. Math. Soc. 314, 661–692.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© CRC Press LLC 1997

Authors and Affiliations

  • Carlos Pérez
    • 1
  1. 1.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain

Personalised recommendations