Tangential-exceptional sets for Hardy-Sobolev spaces
A characterization of the Hardy-Sobolev spaces \(H^ p_ \alpha\) is obtained in terms of a fractional Cauchy-type transform of functions in \(L^ p (d \sigma)\). As a consequence there are obtained some geometric conditions for a set \(E\) in the unit sphere of \(\mathbb{C}^ n\) to be tangential-exceptional for a function in \(H^ p_ \alpha\), \(\alpha p < n\). For the extreme case \(\alpha p = n\) it is given a necessary condition and some examples which show the accuracy of that condition.
scientific article; zbMATH DE number 711025