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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0259134-8
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.


References [Enhancements On Off] (What's this?)

  • [1] J. G. Caughran, Factorization of analytic functions with $ {H^p}$ derivative, Duke Math. J. 36 (1969), 153-158. MR 39 #454. MR 0239095 (39:454)
  • [2] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 24 #A2844. MR 0133008 (24:A2844)
  • [3] P. Novinger, Holomorphic functions with infinitely differentiable boundary values, Illinois J. Math. (to appear). MR 0269861 (42:4754)
  • [4] B. A. Taylor and D. L. Williams, The peak sets of $ {A^m}$, Proc. Amer. Math. Soc. 24 (1970), 604-606. MR 0255828 (41:488)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0259134-8
Keywords: Analytic functions, Hardy classes, zero sets, Carleson set, peak sets
Article copyright: © Copyright 1970 American Mathematical Society

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