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Boundary zeros of functions with derivative in $ H\sp{p}$

Authors: D. J. Caveny and W. P. Novinger
Journal: Proc. Amer. Math. Soc. 25 (1970), 776-780
MSC: Primary 30.67
MathSciNet review: 0259134
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Abstract: It is known that the set of boundary zeros of a function, analytic in the unit disc and with derivative in the Hardy class $ {H^p}$, is a Carleson set provided $ p > 1$. In this paper a proof is given which includes the case $ p = 1$. Peak sets for such functions are investigated and sufficient conditions on subsets of the boundary are given, which guarantee that they are peak sets.

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Keywords: Analytic functions, Hardy classes, zero sets, Carleson set, peak sets
Article copyright: © Copyright 1970 American Mathematical Society

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