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

Sergei Treil | Zendy; Alexander Volberg | Zendy; Dechao Zheng | Zendy

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

Author(s) -

Sergei Treil,

Alexander Volberg,

Dechao Zheng

Publication year - 1997

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/223

Subject(s) - toeplitz matrix , mathematics , invariant (physics) , hilbert transform , pure mathematics , hankel matrix , operator theory , hankel transform , algebra over a field , mathematical analysis , fourier transform , mathematical physics , statistics , spectral density

In this paper, several sufficient conditions for boundedness of the Hilbert transform between two weighted Lp-spaces are obtained. Invariant A8 weights are obtained. Several characterizations of invariant A8 weights are given. We also obtain some sufficient conditions for products of two Toeplitz operators of Hankel operators to be bounded on the Hardy space of the unit circle using Orlicz spaces and Lorentz spaces.

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