Vol. 42, No. 1, 1972

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On the range sets of Hp functions

Leon Brown and Lowell J. Hansen

Vol. 42 (1972), No. 1, 27–32
Abstract

The object of this paper is to show that, even though every function in Hp(0 < p < ) has a nontangential limit almost everywhere, “most” functions in Hp have surprisingly “wild” behavior at the boundary. The proof uses category arguments and a method of constructing non-normal functions in Hp.

Mathematical Subject Classification
Primary: 30A18
Secondary: 30A72
Milestones
Received: 16 April 1961
Revised: 22 December 1971
Published: 1 July 1972
Authors
Leon Brown
Lowell J. Hansen