Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-12T19:32:50.408Z Has data issue: false hasContentIssue false
  • English
  • Français

The essential norms of composition operators

Published online by Cambridge University Press:  18 May 2009

Boo Rim Choe
Boo Rim Choe
Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Kusong-Dong 373-1, Yusong-Gu, Taejon 305-701, Korea
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Throughout the paper n denotes a fixed positive integer unless otherwise specified. Let B = Bn denote the open unit ball of ℂn and let S = Sn denote its boundary, the unit sphere. The unique rotation-invariant probability measure on 5 will be denoted by σ = σn. For n = l, we use more customary notations D = B1, T = S1 and dσ1= dθ/2π. The Hardy space on B, denoted by H2(B), is then the space of functions f holomorphic on B for which

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992, pp. 143 - 155
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Carleson, L., Interpolation by bounded analytic functions and the corona problem, Ann. of Math., 76 (1962), 547–559.CrossRefGoogle Scholar
2.Choe, B., Composition property of holomorphic functions on the ball, Michigan Math. J., 36 (1989), 289–301.CrossRefGoogle Scholar
3.Choe, B., Weights induced by homogeneous polynomials, Pacific J. Math., 139 (1989), 225–240.CrossRefGoogle Scholar
4.Cima, J. and Wogen, W., A Carleson measure theorem for the Bergman space on the ball, J. Operator Theory, 7 (1982), 157–165.Google Scholar
5.Cowen, C., Linear fractional composition operators on H2, Integral equations Operator theory, 11 (1988), 151–160.CrossRefGoogle Scholar
6.Hasting, W., A Carleson measure theorem for Bergman spaces. Proc. Amer. Math. Soc., 52 (1975), 237–241.CrossRefGoogle Scholar
7.Hörmander, L., Lv estimates for (pluri-)subharmonic functions, Math. Scand., 20 (1967), 65–78.CrossRefGoogle Scholar
8.MacCluer, B., Compact composition operators on Hp(Bn) Michigan Math. J., 32 (1985), 237–248.CrossRefGoogle Scholar
9.MacCluer, B. and Shapiro, J., Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math., 38 (1986), 878–906.CrossRefGoogle Scholar
10.Nordgren, E., Composition operators, Canad. J. Math., 20 (1968), 442–449.CrossRefGoogle Scholar
11.Power, S., Hormander's Carleson theorem for the ball, Glasgow Math. J., 26 (1985), 13–17.CrossRefGoogle Scholar
12.Rudin, W., Composition with inner functions, Complex Variables, 4 (1984), 7–19.Google Scholar
13.Rudin, W., Function theory in the unit ball of ℂn, (Springer-Verlag, 1980).CrossRefGoogle Scholar
14.Rudin, W., New constructions of functions holomorphic in the unit ball of ℂn, CBMS Regional Conf. Ser. in Math., No. 63, Amer. Math. Soc, 1986.CrossRefGoogle Scholar
15.Ryff, J., Subordinate Hp functions, Duke Math. J., 33 (1966), 347–354.CrossRefGoogle Scholar
16.Shapiro, J., The essential norm of a composition operator, Ann. of Math., 125 (1987), 375–404.CrossRefGoogle Scholar
17.Stegenga, D., Multiplers of the Dirichlet space, Illinois J. Math., 24 (1980), 113–139.CrossRefGoogle Scholar
18.Tomaszewski, B., Interpolation and inner maps that preserve measure, J. Fund. Anal., 55 (1984), 63–67.CrossRefGoogle Scholar
19.Weidman, J., Linear operators in Hilbert spaces, (Springer-Verlag, 1980).CrossRefGoogle Scholar