JournalsrmiVol. 13, No. 2pp. 319–360

Hilbert transform, Toeplitz operators and Hankel operators, and invariant AA_\infty weights

  • Sergei Treil

    Brown University, Providence, USA
  • Alexander Volberg

    Michigan State University, East Lansing, USA
  • Dechao Zheng

    Vanderbilt University, Nashville, USA
Hilbert transform, Toeplitz operators and Hankel operators, and invariant $A_\infty$ weights cover
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Abstract

In this paper several sufficient conditions for boundedness of the Hilbert transform between two weighted LpL^p-spaces are obtained. Invariant AA_\infty weights are introduced. Several characterizations of invariant AA_\infty weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators or Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.

Cite this article

Sergei Treil, Alexander Volberg, Dechao Zheng, Hilbert transform, Toeplitz operators and Hankel operators, and invariant AA_\infty weights. Rev. Mat. Iberoam. 13 (1997), no. 2, pp. 319–360

DOI 10.4171/RMI/223