An extremal property of the Bloch space
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- by Lee A. Rubel and Richard M. Timoney PDF
- Proc. Amer. Math. Soc. 75 (1979), 45-49 Request permission
Abstract:
The Bloch space $\mathcal {B}$ is the space of functions f analytic in the unit disc D such that $|f’(z)|(1 - |z{|^2})$ 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
- J. M. Anderson, J. Clunie, and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12–37. MR 361090
- G. M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, American Mathematical Society, Providence, R.I., 1969. MR 0247039
- L. A. Rubel and B. A. Taylor, Functional analysis proofs of some theorems in function theory, Amer. Math. Monthly 76 (1969), 483–489; correction, ibid. 77 (1969), 58. MR 0247115
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841 R. M. Timoney, Bloch functions in several complex variables, Thesis, Univ. of Illinois at Urbana-Champaign, 1978.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 45-49
- MSC: Primary 30D99; Secondary 32A10, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529210-9
- MathSciNet review: 529210