Let $\theta$ be an inner function satisfying the connected level set condition of B. Cohn, and let $K^{ 1}_{ \theta}$ be the shift-coinvariant subspace of the Hardy space $H^1$ generated by $\theta$. We describe the dual space to $K^{ 1}_{ \theta}$ in terms of a bounded mean oscillation with respect to the Clark measure $\sigma_\alpha$ of $\theta$. Namely, we prove that $(K^{ 1}_{ \theta} \cap zH^1)^* = { \rm BMO}(\sigma_\alpha)$. The result implies a two-sided estimate for the operator norm of a finite Hankel matrix of size $n\times n$ via ${ \rm BMO}(\mu_{ 2n})$-norm of its standard symbol, where $\mu_{ 2n}$ is the Haar measure on the group $\{ \xi \in \mathbb{ C}: \xi^{ 2n} = 1\}$.
Categories: math.CV