Harmonic functions having no tangential limits

Abstract

Let C 0 {C_0} be a tangential curve in D = { | z | > 1 } D = \left \{ {|z| > 1} \right \} which ends at 1 and let C θ {C_\theta } be its rotation about the origin through an angle θ \theta . We construct a bounded harmonic function in D D which fails to have limits along C θ {C_\theta } for all θ , 0 ≤ θ ≤ 2 π \theta ,0 \leq \theta \leq 2\pi .