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Generalized Schwarz-Pick estimates

Author(s): Barbara D. MacCluer; Karel Stroethoff; Ruhan Zhao
Journal: Proc. Amer. Math. Soc. 131 (2003), 593-599.
MSC (2000): Primary 30C80, 47B33
Posted: June 12, 2002
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Abstract | References | Similar articles | Additional information

Abstract: We obtain higher derivative generalizations of the Schwarz-Pick inequality for analytic self-maps of the unit disk as a consequence of recent characterizations of boundedness and compactness of weighted composition operators between Bloch-type spaces.

References:

1.: C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995. MR 97i:47056
2.: K.M. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), 2679-2687. MR 95i:47061
3.: S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mountain Math. J., to appear.
4.: S. Roman, The Formula of Faà di Bruno, Amer. Math. Monthly 87 (1980), 805-809. MR 82d:26003
5.: K. Zhu, Operator Theory in Function Spaces, M. Dekker, New York, 1990. MR 92c:47031

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Additional Information:

Barbara D. MacCluer
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: bdm3f@virginia.edu

Karel Stroethoff
Affiliation: Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812
Email: ma_kms@selway.umt.edu

Ruhan Zhao
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Address at time of publication: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221

DOI: 10.1090/S0002-9939-02-06588-7
PII: S 0002-9939(02)06588-7
Received by editor(s): July 19, 2001
Received by editor(s) in revised form: October 2, 2001
Posted: June 12, 2002
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2002, American Mathematical Society


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