On the Duality of Hardy Spaces NearH1

Abstract

We are concerned with the duality of the Hardy subspaces of function spaces which behave like L 1 in the sense that the Riesz projection is unbounded. It is shown that the theorem of Fefferman which describes the dual of H 1 as being the space of balayages of Carleson measures extends most naturally to a class of function spaces that was introduced by Lorentz.