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

DOI:
https://doi.org/10.1090/S0002-9939-1979-0529210-9

MathSciNet review:
529210

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Bloch space is the space of functions *f* analytic in the unit disc *D* such that is bounded. It is shown that 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.

**[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)****[2]**G. M. Goluzin,*Geometric theory of functions of a complex variable*, Transl. Math. Monos., vol. 26, Amer. Math. Soc., Providence, R. I., 1969. MR**0247039 (40:308)****[3]**L. A. Rubel and B. A. Taylor,*Functional analysis proofs of some theorems in function theory*, Amer. Math. Monthly**76**(1969), 483-489. MR**0247115 (40:384)****[4]**W. Rudin,*Function theory in polydiscs*, Benjamin, New York, 1969. MR**0255841 (41:501)****[5]**R. M. Timoney,*Bloch functions in several complex variables*, Thesis, Univ. of Illinois at Urbana-Champaign, 1978.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
30D99,
32A10,
46E15

Retrieve articles in all journals with MSC: 30D99, 32A10, 46E15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0529210-9

Article copyright:
© Copyright 1979
American Mathematical Society