Revista Matemática Iberoamericana


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Volume 13, Issue 2, 1997, pp. 319–360
DOI: 10.4171/RMI/223

Published online: 1997-08-31

Hilbert transform, Toeplitz operators and Hankel operators, and invariant $A_\infty$ weights

Sergei Treil[1], Alexander Volberg[2] and Dechao Zheng[3]

(1) Brown University, Providence, USA
(2) Michigan State University, East Lansing, USA
(3) Vanderbilt University, Nashville, USA

In this paper several sufficient conditions for boundedness of the Hilbert transform between two weighted $L^p$-spaces are obtained. Invariant $A_\infty$ weights are introduced. Several characterizations of invariant $A_\infty$ 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.

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Treil Sergei, Volberg Alexander, Zheng Dechao: Hilbert transform, Toeplitz operators and Hankel operators, and invariant $A_\infty$ weights. Rev. Mat. Iberoam. 13 (1997), 319-360. doi: 10.4171/RMI/223