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A constructive proof of the Fefferman-Stein decomposition of BMO (R n)

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Acta Mathematica

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References

  1. Calderón, A. P., An atomic decomposition of distributions in parabolicH p spaces.Adv. in Math., 25 (1977), 216–225.

    Article  MATH  Google Scholar 

  2. Calderón, A. P. &Torchinsky, A., Parabolic maximal functions associated with a distribution.Adv. in Math., 16 (1975), 1–63.

    Article  MATH  Google Scholar 

  3. Carleson, L., Two remarks onH 1 and BMO.Adv. in Math., 22 (1976), 269–277.

    Article  MATH  MathSciNet  Google Scholar 

  4. — An explicit unconditional basis inH 1.Bull. Sci. Math., 104 (1980), 405–416.

    MATH  MathSciNet  Google Scholar 

  5. Chang, S.-Y. &Fefferman, R., A continuous version of duality ofH 1 and BMO on the bidisc.Ann. of Math., 112 (1980), 179–201.

    Article  MATH  MathSciNet  Google Scholar 

  6. Coifman, R. &Dahlberg, B., Singular integral charcterization of nonisotropicH p spaces and the F. and M. Riesz theorem.Proc. Symp. Pure Math., 35 (1979), 231–234.

    MATH  MathSciNet  Google Scholar 

  7. Coifman, R. &Weiss, G., Extensions of Hardy spaces and their use in analysis,Bull Amer. Math. Soc. 83 (1977), 569–645.

    MATH  MathSciNet  Google Scholar 

  8. Fefferman, C. &Stein, E. M.,H p spaces of several variables,Acta Math., 129 (1972), 137–193.

    Article  MATH  MathSciNet  Google Scholar 

  9. Gandulfo, A., Garcia-Cuerva, J. &Taibleson, M., Conjugate system characterization ofH 1: counter examples for the Euclidean plane and local fields.Bull. Amer. Math. Soc., 82 (1976), 83–85.

    Article  MATH  MathSciNet  Google Scholar 

  10. Janson, S., Characterization ofH 1 by singular integral transforms on martingales andR n.Math. Scand., 41 (1977), 140–152.

    MATH  MathSciNet  Google Scholar 

  11. Jones, P. W.,Constructions with functions of bounded mean oscillation. Ph.D. Thesis. University of California, 1978.

  12. —, Carleson measures and the Fefferman-Stein decomposition of BMO (R),Ann. of Math., 111 (1980), 197–208.

    Article  MATH  MathSciNet  Google Scholar 

  13. Jones, P. W. L estimates for the\(\bar \partial \) problem in a half-plane. To appear in Acta Math.

  14. Stein, E. M.,Singular integrals and differentiability properties of functions. Princeton, 1970.

  15. Uchiyama, A., A constructive proof of the Fefferman-Stein decomposition of BMO on simple martingales. To appear in theProceedings of the conference in honor of Antoni Zygmund, held at the University of Chicago, 1981.

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This work was supported in part by Science Research Foundation of Japan. (General Research (c) 1980.)

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Uchiyama, A. A constructive proof of the Fefferman-Stein decomposition of BMO (R n). Acta Math 148, 215–241 (1982). https://doi.org/10.1007/BF02392729

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