Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 2 (2018), 374-398.
A generalized Hilbert operator acting on conformally invariant spaces
If is a positive Borel measure on the interval , we let be the Hankel matrix with entries , where, for , denotes the moment of order of . This matrix formally induces the operator
on the space of all analytic functions , in the unit disk . This is a natural generalization of the classical Hilbert operator. The action of the operators on Hardy spaces has been recently studied. This article is devoted to a study of the operators 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 -spaces.
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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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. https://projecteuclid.org/euclid.bjma/1504857614