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A constructive proof of the Fefferman-Stein decomposition of BMO(R**n). (English) Zbl 0514.46018

##### MSC:
 4.6e+31 Spaces of measurable functions
##### Keywords:
Fefferman-Stein decomposition; constructive proof; BMO
##### References:
 [1] Calderón, A. P., An atomic decomposition of distributions in parabolicH p spaces.Adv. in Math., 25 (1977), 216–225. · Zbl 0379.46050 · doi:10.1016/0001-8708(77)90074-3 [2] Calderón, A. P. &Torchinsky, A., Parabolic maximal functions associated with a distribution.Adv. in Math., 16 (1975), 1–63. · Zbl 0315.46037 · doi:10.1016/0001-8708(75)90099-7 [3] Carleson, L., Two remarks onH 1 and BMO.Adv. in Math., 22 (1976), 269–277. · Zbl 0357.46058 · doi:10.1016/0001-8708(76)90095-5 [4] – An explicit unconditional basis inH 1.Bull. Sci. Math., 104 (1980), 405–416. [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. · Zbl 0451.42014 · doi:10.2307/1971324 [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. [7] Coifman, R. &Weiss, G., Extensions of Hardy spaces and their use in analysis,Bull Amer. Math. Soc. 83 (1977), 569–645. · Zbl 0358.30023 · doi:10.1090/S0002-9904-1977-14325-5 [8] Fefferman, C. &Stein, E. M.,H p spaces of several variables,Acta Math., 129 (1972), 137–193. · Zbl 0257.46078 · doi:10.1007/BF02392215 [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. · Zbl 0328.42012 · doi:10.1090/S0002-9904-1976-13969-9 [10] Janson, S., Characterization ofH 1 by singular integral transforms on martingales andR n .Math. Scand., 41 (1977), 140–152. [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. · Zbl 0416.30030 · doi:10.2307/1971197 [13] Jones, P. W. L estimates for the $\overline{\partial }$ 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.