RT Journal Article
T1 Hilbert-type operator induced by radial weight on Hardyspaces
A1 Merchán-Álvarez, Noel
A1 Peláez-Márquez, José Ángel
A1 De la Rosa, Elena
K1 Matemáticas aplicadas
K1 Hardy, Espacios de
AB We consider the Hilbert-type operator defined byHω(f)(z)=∫10f(t)(1z∫z0Bωt(u)du)ω(t)dt,where {Bωζ}ζ∈Dare 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 ifsup0≤r<1ωˆ(r)ωˆ(1+r2)<∞,(†)andsup0<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 andsupr∈[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.
PB Springer Nature
YR 2023
FD 2023-09-19
LK https://hdl.handle.net/10630/27799
UL https://hdl.handle.net/10630/27799
LA eng
NO 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
NO Funding for open access charge: Universidad de Málaga / CBUAFunding for open access publishing: Universidad Málaga/CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 19 ene 2026