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Composition with a Nonhomogeneous Bounded Holomorphic Function on the Ball

Published online by Cambridge University Press:  20 November 2018

Jun Soo Choa  and
Hong Oh Kim
Jun Soo Choa
Affiliation:
Korea Advanced Institute of Science and Technology, Seoul, Korea
Hong Oh Kim
Affiliation:
Korea Advanced Institute of Science and Technology, Seoul, Korea
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For an integer n > 1, the letters U and Bn denote the open unit disc in C and the open euclidean unit ball in Cn, respectively. It is known that the homogeneous polynomials

where bα is chosen so that , have the following pull-back property:

If g ∈ ℬ(U) the Block space, then , the space of hoiomorphic functions on Bn of bounded mean oscillation, forand.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 870 - 881
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Ahern, P., On the behavior near a torus of functions holomorphic in the ball, Pacific J. Math. 107 1983, 267–278.Google Scholar
2. Ahern, P.and Rudin, W., Bloch functions, BMO, and boundary zeros, Indiana Univ. Math. J. 36 (1987), 131–148.Google Scholar
3. Choe, B. R., Cauchy integral equalities and applications, preprint.Google Scholar
4. Coifman, R. R., Rochberg, R.and Weiss, G., Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611–635.Google Scholar
5. Pommerenke, C., On Bloch functions, J. London Math. Soc. 2 (1970), 689–695.Google Scholar
6. Rammey, W.and Ullrich, D., The pointwise Fatou theorem and its converse for positive pluriharmonic functions, Duke Math. J. 49 (1982), 655–675.Google Scholar
7. Rudin, W., Function theory in the unit ball of Cn, (Springer-Verlag, New York and Berlin, 1980).Google Scholar
8. Russo, P., Boundary behavior of BMO (Bn), Trans. AMS, 292 (1985), 733–740.Google Scholar