Geodesic
$L^p$-bounded point evaluations for polynomials and uniform rational approximation
Algebra i analiz, Tome 22 (2010) no. 1, pp. 57-74.

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A connection is established between uniform rational approximation, and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane $\mathbb C$. Peak points for $R(X)$ and bounded point evaluations for $H^p(X,dA)$, $1\leq p\infty$, play a fundamental role.
Keywords: polynomial and rational approximation, capacity, peak points, point evaluations. 
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J. E. Brennan; E. R. Militzer. $L^p$-bounded point evaluations for polynomials and uniform rational approximation. Algebra i analiz, Tome 22 (2010) no. 1, pp. 57-74. http://geodesic.mathdoc.fr/item/AA_2010_22_1_a1/

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