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Proceedings of the American Mathematical Society

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



Average radial limits in weighted Hardy spaces

Authors: Alec Matheson and David C. Ullrich
Journal: Proc. Amer. Math. Soc. 97 (1986), 691-694
MSC: Primary 30D40; Secondary 30D50
MathSciNet review: 845989
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Abstract: Weighted Hardy spaces are defined in the unit disc by specifying the rate of growth of $ p$th means near the boundary. Although a function in one of these spaces need have no radial limits, it is shown that in certain of these spaces "average radial limits" exist over an interval on the boundary. An integral representation in terms of these average radial limits is given, with an application to the question of existence of (pointwise) radial limits.

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Article copyright: © Copyright 1986 American Mathematical Society

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