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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Construction of an inner function in the little Bloch space


Author: Kenneth Stephenson
Journal: Trans. Amer. Math. Soc. 308 (1988), 713-720
MSC: Primary 30D50
MathSciNet review: 951624
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Abstract: An explicit construction using Riemann surfaces and Brownian motion is given for an inner function in the unit disc which is not a finite Blaschke product yet belongs to the little Bloch space $ {\mathcal{B}_0}$. In addition to showing how an inner function can meet the geometric conditions for $ {\mathcal{B}_0}$, this example settles an open question concerning the finite ranges of inner functions: the values which it takes only finitely often are dense in the disc.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0951624-3
Article copyright: © Copyright 1988 American Mathematical Society