Maximal Functions and H p Spaces Defined by Ergodic Transformations
Ronald R. Coifman, Guido Weiss · Proceedings of the National Academy of Sciences · 1973
Suppose an ergodic flow acts on a probability space enabling us to introduce the Ergodic Hilbert transform f of f in L(p)(), 1 <== p <== infinity. H(1) is the class of all functions of the form f + if in L(1)(). We show that H(1) can be characterized in terms of a class of maximal functions; moreover, the dual space of H(1) is identified with a space of functions of bounded mean oscillation defined in terms of the flow.