A NOTE ON Lp-BOUNDED POINT EVALUATIONS FOR POLYNOMIALS

We construct a compact nowhere dense subset K of the closed unit disk (D) over bar in the complex plane C such that R(K) = C(K) and bounded point evaluations for P-t(dA vertical bar(K)), 1 <= t < infinity, is the open unit disk D. In fact, there exists C = C(t) > 0 such that integral(D) vertical bar p vertical bar(t) dA <= C integral(K) vertical bar p vertical bar(t) dA, for 1 <= t < infinity and all polynomials p.