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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Boundary zeros of functions with derivative in $H^{p}$
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by D. J. Caveny and W. P. Novinger
Proc. Amer. Math. Soc. 25 (1970), 776-780
DOI: https://doi.org/10.1090/S0002-9939-1970-0259134-8

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.
References
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 776-780
  • MSC: Primary 30.67
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0259134-8
  • MathSciNet review: 0259134