Average radial limits in weighted Hardy spaces

Matheson, Alec; Ullrich, David C.

doi:10.1090/S0002-9939-1986-0845989-4

Average radial limits in weighted Hardy spaces
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by Alec Matheson and David C. Ullrich

Proc. Amer. Math. Soc. 97 (1986), 691-694

DOI: https://doi.org/10.1090/S0002-9939-1986-0845989-4

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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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