A boundary value problem for
Author: Rotraut Goubau Cahill
Journal: Proc. Amer. Math. Soc. 67 (1977), 241-247
MSC: Primary 30A72; Secondary 26A24
MathSciNet review: 0457728
Abstract: Let be an subset of the unit circle of measure 0 and let , be a decreasing sequence with and . There exists an H in of norm whose modulus has radial limit along every radius which has radial limit of modulus on and on . If W is simultaneously a set, H may be chosen to have no zeros on C. It follows that for W countable, say , there is such an H of norm 1 for which . The proof of the theorem depends on the existence of a special collection of closed sets , real, for which the function h, defined by , is such that the function du has the required properties. Some of the techniques used are similar to those developed in an earlier paper .
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-  Zygmunt Zahorski, Über die Menge der Punkte in welchen die Ableitung unendlich ist, Tôhoku Math. J. 48 (1941), 321–330 (German). MR 0027825