On Nontangential Limits and Shift Invariant Subspaces

In 1998, John B. Conway and Liming Yang wrote a paper in which they posed a number of open questions regarding the shift on $P^t(μ)$ spaces. A few of these have been completely resolved, while at least one remains wide open. In this paper, we review some of the solutions, mention some alternate approaches and discuss further the problem that remains unsolved.