Proceedings of the American Mathematical Society

Author(s): Evgueni Doubtsov
Journal: Proc. Amer. Math. Soc. 129 (2001), 3495-3499.
MSC (2000): Primary 47B38
Posted: July 10, 2001
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We apply Leibenzon's backward shift to show that the composition operator on the unit ball of $\mathbb{C}^n$ always maps the weighted Hardy space $H^2_{1-n}$ into the Hardy class

1.

C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995. MR 97i:47056

2.

J.A. Cima and P.R. Mercer, Composition operators between Bergman spaces on convex domains in $\mathbb{C}^n$ , J. Operator Theory 33 (1995), 363-369. MR 96h:47036

3.

G.M. Henkin, Approximation of functions on pseudoconvex domains and Leibenzon's theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 37-42. MR 44:4234

4.

B.D. MacCluer, Compact composition operators on $H\sp p(B\sb N)$ , Michigan Math. J. 32 (1985), 237-248. MR 86g:47037

5.

B.D. MacCluer and P.R. Mercer, Composition operators between Hardy and weighted Bergman spaces on convex domains in $\mathbb{C}^n$ , Proc. Amer. Math. Soc. 123 (1995), 2093-2102. MR 95i:47060

6.

J.H. Shapiro, Composition operators and classical function theory,

Springer-Verlag, New York, 1993. MR 94k:47049

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