For a nonnegative integrable weight function w on the unit circle T, we provide an expression for p = 2, in terms of the series coefficients of the outer function of w, for the weighted Lp distance inff |1-f|pwd, where is the normalized Lebesgue measure and f ranges over trigonometric polynomials with frequencies in [{.,-3,-2,-1}{-n}]u{m}, m 0, n = 2. The problem is open for p = 2. 2006 American Mathematical Society.
