Maximal functions and h spaces defined by ergodic transformations.
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.
Department of Mathematics, Washington University, St. Louis, Missouri 63130.
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Coifman
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Weiss