On the range sets of H^p functions

Leon Brown and Lowell J. Hansen

Vol. 42 (1972), No. 1, 27–32

DOI: 10.2140/pjm.1972.42.27

Abstract

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

Mathematical Subject Classification

Primary: 30A18

Secondary: 30A72

Milestones

Received: 16 April 1961

Revised: 22 December 1971

Published: 1 July 1972