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References
H.Arai, Hardy spaces of 2-parameter Brownian martingales. To appear in Tokyo J. Math.
J. Brossard etL. Chevalier, Calcul stochastiques et inégalités de norme pour les martingales bi-browniennes; application aux fonctions bi-harmoniques. Ann. Inst. Fourier30, 97–120 (1980).
L. Carleson, Interpolation by bounded analytic functions and the corona problem. Ann. of Math.76, 547–559 (1962).
L.Carleson, A counterexample for measures bounded onH p for the bi-disc. Mittag-Leffler Report 7, 1974.
S.-Y. A. Chang, Carleson measure on the bi-disc. Ann. of Math.109, 613–620 (1979).
B. E. J. Dahlberg, On the Poisson integral for Lipschitz andC 1 domains. Studia Math.66, 13–24 (1979).
E.Decamp, Caractérisation des espaces BMO de martingales dyadiques à deux indices, et de fonctions bi-harmoniques surR 2+ ×R 2+ . Thèse de doctorat de 3e cycle, Grenoble 1979.
C. Fefferman andE. M. Stein,H p spaces of several variables. Acta Math.129, 138–193 (1972).
R. Fefferman, Bounded mean oscillation on polydisc. Ann. of Math.110, 395–496 (1979).
R. F. Gundy andE. M. Stein,H p theory for the poly-disc. Proc. Natl. Acad. Sci. USA (3)76, 1026–1029 (1979).
L. L.Helms, Introduction to Potential Theory. New York 1969.
L. Hörmander,L p estimates for (pluri-) subharmonic functions. Math. Scand.20, 65–78 (1967).
D. S. Jerison andC. E. Kenig, Boundary behaviour of harmonic functions in non-tangentially accessible domains. Adv. in Math.46, 80–147 (1982).
P. Jones, Extension theorem for BMO. Indiana Univ. Math. J.29, 41–66 (1980).
S. C.Port andStone, Brownian Motion and Classical Potential Theory. New York-London 1978.
H.Sato, Caractérisation par les transformations de Riesz de la classe de HardyH 1 de fonctions bi-harmoniques surR m+1+ ×R n+1+ . Thèse de doctrat de 3e cycle, Grenoble 1979.
E. M.Stein, Singular Integrals and Differential Properties of Functions. Princeton 1970.
E. M. Stein, A variant of the area integral. Bull. Sci. Math. 2e Série103, 449–461 (1979).
E. L.Stout, The Theory of Uniform Algebras. Belmont, California, 1971.
N. Th. Varopoulos, The Helson-Szegö theorem andA p -functions for Brownian motion and several variables, J. Funct. Anal.39, 85–121 (1980).
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Arai, H. Carleson measures on product domains and 2-parameter Brownian martingales. Arch. Math 46, 343–352 (1986). https://doi.org/10.1007/BF01200465
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DOI: https://doi.org/10.1007/BF01200465