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An extremal property of the Bloch space

Authors: Lee A. Rubel and Richard M. Timoney
Journal: Proc. Amer. Math. Soc. 75 (1979), 45-49
MSC: Primary 30D99; Secondary 32A10, 46E15
MathSciNet review: 529210
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Abstract: The Bloch space $ \mathcal{B}$ is the space of functions f analytic in the unit disc D such that $ \vert f'(z)\vert(1 - \vert z{\vert^2})$ is bounded. It is shown that $ \mathcal{B}$ is the largest Möbius-invariant linear space of analytic functions that can be equipped with a Möbius-invariant seminorm in such a way that there is at least one ``decent'' continuous linear functional on the space. The term ``decent'' has a simple and precise definition.

References [Enhancements On Off] (What's this?)

  • [1] J. M. Anderson, J. G. Clunie and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12-37. MR 0361090 (50:13536)
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  • [5] R. M. Timoney, Bloch functions in several complex variables, Thesis, Univ. of Illinois at Urbana-Champaign, 1978.

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Article copyright: © Copyright 1979 American Mathematical Society

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