Boundary zeros of functions with derivative in 𝐻^{𝑝}

Caveny, D. J.; Novinger, W. P.

doi:10.1090/S0002-9939-1970-0259134-8

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

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.

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