On an extremal property of Doob's class

Author:
J. S. Hwang

Journal:
Trans. Amer. Math. Soc. **252** (1979), 393-398

MSC:
Primary 30D99

MathSciNet review:
534128

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Abstract: Recently, we have solved a long open problem of Doob (1935). To introduce the result proved here, we say that a function belongs to Doob's class *D*, if is analytic in the unit disk *U* and has radial limit zero at an endpoint of some arc *R* on the unit circle such that , where is an arbitrary sequence of points in *U* tending to an arbitrary interior point of *R*.

With this definition, our main result is the following extremal property of Doob's class.

Theorem. , where .

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DOI:
https://doi.org/10.1090/S0002-9947-1979-0534128-6

Keywords:
Extremal property and Doob's class

Article copyright:
© Copyright 1979
American Mathematical Society