On the Duality of Hardy Spaces NearH1

We are concerned with the duality of the Hardy subspaces of function spaces which behave likeL1in the sense that the Riesz projection is unbounded. It is shown that the theorem of Fefferman which describes the dual ofH1as being the space of balayages of Carleson measures extends most naturally to a class of function spaces that was introduced by Lorentz.