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Interpolating sequences for the derivatives of Bloch functions

Published online by Cambridge University Press:  18 May 2009

K. R. M. Attele
K. R. M. Attele
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
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Abstract

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We prove that sufficiently separated sequences are interpolating sequences for f′(z)(1−|z|2) where f is a Bloch function. If the sequence {zn} is an η net then the boundedness f′(z)(1−|z|2) on {zn} is a sufficient condition for f to be a Bloch function. The essential norm of a Hankel operator with a conjugate analytic symbol acting on the Bergman space is shown to be equivalent to .

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 35 - 41
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Amar, Eric, Suites d'interpolation pour les classes de Bergman de la boule e du polydisque de Cn, Canadian J. Math. 30 (1978), 711–737.Google Scholar
2.Anderson, J. M., Clunie, J., and Pommerenke, Ch., On Bloch functions and normal functions, J. Reine und Angew. Math. 270 (1974), 12–37.Google Scholar
3.Axler, Sheldon, The Bergman space, the Bloch space and the commutators of multiplication operators, Duke J. Math. 53 (1986), 315–332.CrossRefGoogle Scholar
4.Axler, Sheldon, Bergman spaces and their operators, Surveys of some Recent Results in Operator Theory, Vol. 1 (Conway, John B. and Morrel, Bernard B., eds.), Pitman Research Notes on Mathematics, 1988, 1–50.Google Scholar
5.Coifman, R., Rochberg, R., and Weiss, G., Factorization theorems for Hardy spaces in several variables, Annals of Math. 103 (1976), 611–635.Google Scholar
6.Garnett, John B., Bounded Analytic Functions (Academic Press, New York, 1981).Google Scholar
7.Luecking, Daniel H., Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives. Amer. J. Math. 107 (1985), 85–111.CrossRefGoogle Scholar
8.Pommerenke, Ch., On Bloch functions, J. London Math. Soc. (2) 2 (1970), 689–695.CrossRefGoogle Scholar