Nontangential limits in Pt(µ)-spaces and the index of invariant subgroups
Abstract Let μ be a finite positive measure on the closed disk D¯ in the complex plane, let 1 ≤ t < ∞, and let Pt(μ) denote the closure of the analytic polynomials in Lt(μ). We suppose that D is the set of analytic bounded point evaluations for Pt(μ), and that Pt(μ) contains no nontrivial characteristic functions. It is then known that the restriction of μ to ∂D must be of the form h|dz|. W