Abstract
If \(\mu \) is a positive Borel measure on the interval [0, 1) we let \(\mathcal H_\mu \) be the Hankel matrix \(\mathcal H_\mu =(\mu _{n, k})_{n,k\ge 0}\) with entries \(\mu _{n, k}=\mu _{n+k}\), where, for \(n\,=\,0, 1, 2, \dots \), \(\mu _n\) denotes the moment of order n of \(\mu \). This matrix induces formally the operator
on the space of all analytic functions \(f(z)=\sum _{k=0}^\infty a_kz^k\), in the unit disc \({\mathbb D}\). This is a natural generalization of the classical Hilbert operator. In this paper we improve the results obtained in some recent papers concerning the action of the operators \(\mathcal {H}_\mu \) on Hardy spaces and on Möbius invariant spaces.
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This research is supported in part by a grant from “El Ministerio de Economía y Competitividad”, Spain (MTM2014-52865-P) and by a grant from la Junta de Andalucía (FQM-210). The second author is also supported by a grant from “El Ministerio de de Educación, Cultura y Deporte”, Spain (FPU2013/01478).
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Girela, D., Merchán, N. A Hankel Matrix Acting on Spaces of Analytic Functions. Integr. Equ. Oper. Theory 89, 581–594 (2017). https://doi.org/10.1007/s00020-017-2409-3
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DOI: https://doi.org/10.1007/s00020-017-2409-3