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oai:riuma.uma.es:10630/277992026-02-03T11:27:03Zcom_10630_2254col_10630_37953

Hilbert-type operator induced by radial weight on Hardyspaces Merchán-Álvarez, Noel Peláez-Márquez, José Ángel De la Rosa, Elena Matemáticas aplicadas Hardy, Espacios de We consider the Hilbert-type operator defined by Hω(f)(z)=∫10f(t)(1z∫z0Bωt(u)du)ω(t)dt, where {Bωζ}ζ∈D are the reproducing kernels of the Bergman space A2ω induced by a radial weight ω in the unit disc D. We prove that Hω is bounded on the Hardy space Hp, 1<p<∞ , if and only if sup0≤r<1ωˆ(r)ωˆ(1+r2)<∞,(†) and sup0<r<1(∫r01ωˆ(t)pdt)1p(∫1r(ωˆ(t)1−t)p′dt)1p′<∞, where ωˆ(r)=∫1rω(s)ds . We also prove that Hω:H1→H1 is bounded if and only if († ) holds and supr∈[0,1)ωˆ(r)1−r(∫r0dsωˆ(s))<∞. As for the case p=∞ , Hω is bounded from H∞ to \mathord \mathrm{BMOA}, or to the Bloch space, if and only if (†) holds. In addition, we prove that there does not exist radial weights ω such that Hω:Hp→Hp, 1≤p<∞, is compact and we consider the action of Hω on some spaces of analytic functions closely related to Hardy spaces. 2023-10-11T06:42:46Z 2023-10-11T06:42:46Z 2023-09-19 journal article Merchán, N., Peláez, J.Á. & de la Rosa, E. Hilbert-type operator induced by radial weight on Hardy spaces. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 2 (2024). https://doi.org/10.1007/s13398-023-01500-z https://hdl.handle.net/10630/27799 https://doi.org/10.1007/s13398-023-01500-z eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature