Two-weight inequality for the Hilbert transform: A real variable characterization, I Academic Article uri icon

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  • The two weight inequality for the Hilbert transform arises in the settings of analytic function spaces, operator theory, and spectral theory, and what would be most useful is a characterization in the simplest real-variable terms. We show that the $L^2$ to $L^2$ inequality holds if and only if two L^2 to weak-L^2 inequalities hold. This is a corollary to a characterization in terms of a two-weight Poisson inequality, and a pair of testing inequalities on bounded functions.


  • Lacey, Michael T
  • Sawyer, Eric
  • Shen, Chun-Yen
  • Uriarte-Tuero, Ignacio

publication date

  • December 2014