Reproducing kernel of the space $R^t(K,μ)$

Abstract

For 1 ≤ t < ∞, a compact subset K of the complex plane C, and a finite positive measure µ supported on K, R t (K, µ) denotes the closure in L t (µ) of rational functions with poles off K. Let Ω be a connected component of the set of analytic bounded point evaluations for R t (K, µ). In this paper, we examine the behavior of the reproducing kernel of R t (K, µ) near the boundary ∂Ω∩T, assuming that µ(∂Ω∩T) > 0, where T is the unit circle.