Model spaces and Toeplitz kernels in reflexive Hardy space (Q2807241)

The paper develops some approaches given in [\textit{M. C. Câmara} and \textit{J. R. Partington}, J. Anal. Math. 124, 235--260 (2014; Zbl 1325.47061)]. Let \(\mathbb D\) be the unit disc in the complex plane. The model spaces are the kernels of Toeplitz operators on the space \(H^{p}(\mathbb D)\) with symbols \(\bar{\theta}\) for inner functions \(\theta\). In the paper under review, these spaces are investigated, and similar spaces in the case of the upper complex plane. Necessary and sufficient conditions for the model space to consist entirely of bounded functions are obtained. The authors give a characterization of maximal functions in a model space, those functions which are contained in no smaller Toeplitz kernels. They investigate kernels of Toeplitz operators whose symbols differ only by an inner factor.