|ISSN 1088-6826(online) ISSN 0002-9939(print)|
A convergence question in
Abstract: Let (unit disc), . and let . If contains a nontrivial inner factor, it is known that is unbounded in -norm. We prove that if is analytic on the closed disc and has no zeros on the open disc, then in , as . The same conclusion follows if . We construct an outer function which is continuous on the closed disc, analytic for , and such that is unbounded in every .
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