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Measures of Carleson type on filtrated probability spaces and the corona theorem on complex Brownian spaces
Author:
Hitoshi Arai
Journal:
Proc. Amer. Math. Soc. 96 (1986), 643-647
MSC:
Primary 60G44; Secondary 46J10, 60G46
MathSciNet review:
826495
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Additional Information
Abstract: N. Th. Varopoulos showed the existence of corona solutions for bounded holomorphic martingales (cf. [7]). In this paper we investigate measures of Carleson type on usual filtrated probability spaces and as its application we estimate the corona solutions by a probabilistic modification of Wolff's approach.
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- H. Arai, On the algebra of bounded holomorphic martingales, Proc. Amer. Math. Soc. (to appear). MR 845975 (87j:46100)
- [2]
- J. B. Garnett, Bounded analytic functions, Academic Press, New York, 1981. MR 628971 (83g:30037)
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- N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland, Amsterdam, 1981. MR 1011252 (90m:60069)
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- P. A. Meyer, Un cours sur les intégrales stochastiques, Lecture Notes in Math., Vol. 511, Springer-Verlag, Berlin and New York, 1976, pp. 245-400. MR 0501332 (58:18721)
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- T. Nakazi, Hardy spaces and Jensen measures, Trans. Amer. Math. Soc. 274 (1982), 375-378. MR 670939 (84a:46110)
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- T. P. Srinivasan and Ju-Kwei Wang, Weak* Dirichlet algebras, Proc. Internat. Sympos. on Function Algebras, Scott-Foresman, Glenview, Ill., 1966, pp. 216-249. MR 0198282 (33:6441)
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- N. Th. Varopoulos, The Helson-Szegö theorem and
 -functions for Brownian motion and several variables, J. Funct. Anal. 39 (1980), 85-121. MR 593791 (82a:60069)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0826495-X
PII:
S 0002-9939(1986)0826495-X
Keywords:
Measure of Carleson type,
BMO-martingale,
holomorphic martingale,
Wolff's theorem,
corona theorem
Article copyright:
© Copyright 1986 American Mathematical Society
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