# Discontinuous bounded holomorphic function

Is there any bounded holomorphic function on the unit disk whose limit (not just radial) exists at all boundary points expect one point?

• What about $e^{\frac{1+z}{z-1}}$? Oct 11 '20 at 5:38
• Thanks! I thought continuity on the boundary (except one point) would somehow release us from the hard-checking condition of Piravalov theorem. Oct 11 '20 at 21:00