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The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus
Author:
Alexander Schuster
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3525-3530
MSC (2000):
Primary 30H05
Posted:
May 31, 2006
MathSciNet review:
2240664
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Abstract: It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.
References
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W. Hayman, On a conjecture of Korenblum, Analysis (Munich) 19 (1999), 195-205. MR 1705360 (2000e:30041)
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A. Hinkkanen, On a maximum principle on Bergman space, J. Analyse Math 79 (1999), 335-344. MR 1749317 (2000m:30033)
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M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter Expositions in Mathematics, 9, Walter de Gruyter & Co., Berlin, 1993.MR 1242120 (94k:32039)
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B. Korenblum, A maximum principle for the Bergman space, Publ. Mat. 35 (1991), 479-486.MR 1201570 (93j:30018)
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C. Wang, Refining the constant in a maximum principle for the Bergman space, Proc. Amer. Math. Soc. 132 (2003), 853-855. MR 2019965 (2004i:30017)
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Additional Information
Alexander Schuster
Affiliation:
Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email:
schuster@sfsu.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08378-X
PII:
S 0002-9939(06)08378-X
Keywords:
Bergman space,
Fock space,
maximum principle
Received by editor(s):
September 15, 2004
Received by editor(s) in revised form:
June 15, 2005
Posted:
May 31, 2006
Communicated by:
Juha M. Heinonen
Article copyright:
© Copyright 2006 American Mathematical Society
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