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

  • 3
    $\begingroup$ What about $e^{\frac{1+z}{z-1}}$? $\endgroup$
    – Conrad
    Oct 11 '20 at 5:38
  • $\begingroup$ Thanks! I thought continuity on the boundary (except one point) would somehow release us from the hard-checking condition of Piravalov theorem. $\endgroup$
    – Hamid Enki
    Oct 11 '20 at 21:00

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