Stolz region (${\Gamma }_A(\xi )=\{z\in \mathbb{D}:|z-\xi |<A(1-|z|)\},A>1$)

A fixed-aperture approach region at a boundary point of the unit disc. Its points approach the boundary point without becoming tangent to the circle. Convergence inside every such fixed region is a nontangential limit; the corresponding supremum defines a non-tangential maximal function.