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

For $1\le t<\mathrm{\infty },$ a compact subset $K$ of the complex plane $\mathbb C,$andafinitepositivemeasure$\mu$supportedon$K,$ $R^t(K,\mu )$ denotes the closure in $L^t(\mu )$ of rational functions with poles off $K$. Let $\mathrm{\Omega }$ be a connected component of the set of analytic bounded point evaluations for $R^t(K,\mu )$. In this paper, we examine the behavior of the reproducing kernel of $R^t(K,\mu )$ near the boundary $\partial \Omega \cap \mathbb T$,assumingthat$\mu (\partial \Omega \cap \mathbb T ) > 0$,where$\mathbb T$ is the unit circle.