, Volume 87, Issue 5, pp 3781-3787

On the existence of nontangential boundary values of pseudocontinuable functions

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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.

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 5–17.