RT Journal Article
T1 Bergman projection induced by radial weight.
A1 Rättyä, Jouni
A1 Peláez-Márquez, José Ángel
K1 Funciones de variable compleja
AB We establish characterizations of the radial weights $\omega$ on the unit disc such that the Bergman projection $P_\omega$, induced by $\omega$, is bounded and/or acts surjectively from $L^\infty$ to the Bloch space $\mathcal{B}$, or the dual of the weighted Bergman space $A^1_\omega$ is isomorphic to the Bloch space under the $A^2_\omega$-pairing. We also solve the problem posed by Dostani\'c in 2004 of describing the radial weights~$\omega$ such that~$P_\omega$ is bounded on the Lebesgue space~$L^p_\omega$, under a weak regularity hypothesis on the weight involved. With regard to Littlewood-Paley estimates, we characterize the radial weights~$\omega$ such that the norm of any function in $A^p_\omega$ is comparable to the norm in $L^p_\omega$ of its derivative times the distance from the boundary. This last-mentioned result solves another well-known problem on the area. All characterizations can be given in terms of doubling conditions on moments and/or tail integrals $\int_r^1\omega(t)\,dt$ of $\omega$, and are therefore easy to interpret.
PB Elsevier
YR 2021
FD 2021
LK https://hdl.handle.net/10630/37190
UL https://hdl.handle.net/10630/37190
LA spa
NO https://openpolicyfinder.jisc.ac.uk/id/publication/10115
NO This research was supported in part by Ministerio de Economía y Competitividad, Spain, projects PGC2018-096166-B-100; La Junta de Andalucía, project FQM210 and UMA18-FEDERJA-002; Academy of Finland project no. 268009; Vilho, Yrjö ja Kalle Foundation
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026