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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Conditions on the logarithmic derivative of a function implying boundedness

Authors: T. H. MacGregor and F. Rønning
Journal: Trans. Amer. Math. Soc. 347 (1995), 2245-2254
MSC: Primary 30C45
MathSciNet review: 1277126
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Abstract: In this paper we investigate functions analytic and nonvanishing in the unit disk, with the property that the logarithmic derivative is contained in some domain $ \Omega $. We obtain conditions on $ \Omega $ which imply that the functions are bounded and that their first derivatives belong to $ {H^p}$ for some $ p \geqslant 1$. For certain domains $ \Omega $ the sufficient conditions that we give are also, in some sense, necessary. Examples of domains to which the results apply are given.

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