A Lower Bound in Nehari ’ S Theorem on the Polydisc

  title={A Lower Bound in Nehari ’ S Theorem on the Polydisc},
  author={Joaquim Ortega-Cerd{\`a} and Kristian Seip},
By theorems of Ferguson and Lacey (d = 2) and Lacey and Terwilleger (d > 2), Nehari’s theorem is known to hold on the polydisc D for d > 1, i.e., if Hψ is a bounded Hankel form on H(D) with analytic symbol ψ, then there is a function φ in L∞(Td) such that ψ is the Riesz projection of φ. A method proposed in Helson’s last paper is used to show that the constant Cd in the estimate ‖φ‖∞ ≤ Cd‖Hψ‖ grows at least exponentially with d; it follows that there is no analogue of Nehari’s theorem on the… CONTINUE READING

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