2026-05-31T21:51:18Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/371902026-02-03T11:23:40Zcom_10630_2254col_10630_37953

Bergman projection induced by radial weight. Rättyä, Jouni Peláez-Márquez, José Ángel Funciones de variable compleja Bergman space Bergman projection Bloch space Bounded mean oscillation Doubling weight Littlewood-Paley formula https://openpolicyfinder.jisc.ac.uk/id/publication/10115 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. 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 2025-01-28T12:23:29Z 2025-01-28T12:23:29Z 2021 journal article AM https://hdl.handle.net/10630/37190 10.1016/j.aim.2021.107950 spa open access application/pdf Elsevier