Abstract
Let θ be an inner function, let θ*(H 2)=H 2⊖θH 2, and let μ be a finite Borel measure on the unit circle\(\mathbb{T}\). Our main purpose is to prove that, if every functionf∈θ*(H 2) can be defined μ-almost everywhere on\(\mathbb{T}\) in a certain (weak) natural sense, then every functionf∈θ*(H 2) has finite angular boundary values μ-almost everywhere on\(\mathbb{T}\). A similar result is true for the Lp-analog of θ*(H 2) (p>0). Bibliography: 17 titles.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 5–17.
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Aleksandrov, A.B. On the existence of nontangential boundary values of pseudocontinuable functions. J Math Sci 87, 3781–3787 (1997). https://doi.org/10.1007/BF02355824
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DOI: https://doi.org/10.1007/BF02355824