Maximal functions and h spaces defined by ergodic transformations.

  title={Maximal functions and h spaces defined by ergodic transformations.},
  author={R R Coifman and Gary Weiss},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  volume={70 6},
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. 

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