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On the universal integral means spectrum of conformal mappings near the origin

Author(s): Håkan Hedenmalm; Serguei Shimorin
Journal: Proc. Amer. Math. Soc. 135 (2007), 2249-2255.
MSC (2000): Primary 30C40; Secondary 30C85, 32A25, 32A36, 46E22
Posted: February 2, 2007
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Abstract: We improve the local estimate near the origin of the integral means spectrum for conformal mappings obtained in our paper from 2005. We also study some algebraic aspects of higher order forms associated with the given conformal mapping.

References:

1.: H. Hedenmalm, I. Kayumov, On Makarov's law of the iterated logarithm, Proc. Amer. Math. Soc., to appear.
2.: H. Hedenmalm, S. Shimorin, Weighted Bergman spaces and the integral means spectrum of conformal mappings, Duke Math. J. 127 (2005), 341-393. MR 2130416 (2005m:30010)
3.: Ch. Pommerenke, Boundary behaviour of conformal maps. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 299. Springer-Verlag, Berlin, 1992. MR 1217706 (95b:30008)

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Additional Information:

Håkan Hedenmalm
Affiliation: Department of Mathematics, Royal Institute of Technology, S--100 44 Stockholm, Sweden
Email: haakanh@math.kth.se

Serguei Shimorin
Affiliation: Department of Mathematics, Royal Institute of Technology, S--100 44 Stockholm, Sweden
Email: shimorin@math.kth.se

DOI: 10.1090/S0002-9939-07-08737-0
PII: S 0002-9939(07)08737-0
Received by editor(s): November 2, 2005
Received by editor(s) in revised form: March 29, 2006
Posted: February 2, 2007
Additional Notes: The first author's research was supported by the Göran Gustafsson Foundation
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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