Banach Journal of Mathematical Analysis

A generalized Hilbert operator acting on conformally invariant spaces

Daniel Girela and Noel Merchán

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If μ is a positive Borel measure on the interval [0,1), we let Hμ be the Hankel matrix Hμ=(μn,k)n,k0 with entries μn,k=μn+k, where, for n=0,1,2,, μn denotes the moment of order n of μ. This matrix formally induces the operator

Hμ(f)(z)=n=0(k=0μn,kak)zn on the space of all analytic functions f(z)=k=0akzk, in the unit disk D. This is a natural generalization of the classical Hilbert operator. The action of the operators Hμ on Hardy spaces has been recently studied. This article is devoted to a study of the operators Hμ acting on certain conformally invariant spaces of analytic functions on the disk such as the Bloch space, the space BMOA, the analytic Besov spaces, and the Qs-spaces.

Article information

Banach J. Math. Anal., Volume 12, Number 2 (2018), 374-398.

Received: 25 December 2016
Accepted: 16 May 2017
First available in Project Euclid: 8 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 30H10: Hardy spaces

Hilbert operators conformally invariant spaces Carleson measures


Girela, Daniel; Merchán, Noel. A generalized Hilbert operator acting on conformally invariant spaces. Banach J. Math. Anal. 12 (2018), no. 2, 374--398. doi:10.1215/17358787-2017-0023.

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