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
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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
- James G. Caughran, Factorization of analytic functions with $H^{p}$ derivative, Duke Math. J. 36 (1969), 153–158. MR 239095
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- W. P. Novinger, Holomorphic functions with infinitely differentiable boundary values, Illinois J. Math. 15 (1971), 80–90. MR 269861, DOI 10.1215/ijm/1256052822
- B. A. Taylor and D. L. Williams, The peak sets of $A^{m}$, Proc. Amer. Math. Soc. 24 (1970), 604–606. MR 255828, DOI 10.1090/S0002-9939-1970-0255828-9
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