Quantitative possibilities for Baxter's theorem in nonlinear Fourier analysis

Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\ell^1$. However, this equivalence is purely qualitat