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

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References

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  4. Coifman, R. (1972). Distribution function inequalities for singular integrals.Proc. Acad. Sci. U.S.A. 69, 2838–2839.

    Article  MATH  MathSciNet  Google Scholar 

  5. Coifman, R., Rochberg, R., and Weiss, G. (1976). Factorization theorems for Hardy spaces in several variables.Ann. of Math.(2)103, 611–635.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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. Greco, L. and Iwaniec, T. (1994). New inequalities for the Jacobian.Ann. Inst. H. Poincare 11, 17–35.

    MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  10. Iwaniec, T. and Sbordone, C. Weak minima of variational integrals.J. Reine Angew Math. 454, 143–161.

  11. Janson, S. (1978). Mean oscillation and commutators of singular integral operators.Ark. Math. 16, 263–270.

    Article  MATH  MathSciNet  Google Scholar 

  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. Milman, M. (1995). Extrapolation and optimal decompositions.Lecture Notes in Math. 1580. Springer-Verlag, New York.

    Google Scholar 

  14. O’Neil, R. (1963). Fractional integration in Orlicz spaces.Trans. Amer. Math. Soc. 115, 300–328.

    Article  MathSciNet  Google Scholar 

  15. O’Neil, R. (1968). Integral transforms and tensor products on Orlicz spaces andL p,q spaces.J. Anal. Math. 21, 1–276.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  17. Pérez, C. (1995). Endpoint estimates for commutators of singular integral operators.J. Funct. Anal. 128, 163–185.

    Article  MATH  MathSciNet  Google Scholar 

  18. Pérez, C. (1994). Weighted norm inequalities for singular integral operators.J. London Math. Soc. 49, 296–308.

    MATH  MathSciNet  Google Scholar 

  19. Rochberg, R. and Weiss, G. (1983). Derivatives of analytic families of Banach spaces.Ann. of Math. (2)118.

  20. Stein, E.M. (1969). Note on the classL logL.Studia Math. 32, 305–310.

    MATH  MathSciNet  Google Scholar 

  21. Wilson, J.M. (1989). Weighted norm inequalities for the continuos square functions.Trans. Amer. Math. Soc. 314, 661–692.

    Article  MATH  MathSciNet  Google Scholar 

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Pérez, C. Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function. The Journal of Fourier Analysis and Applications 3, 743–756 (1997). https://doi.org/10.1007/BF02648265

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