RT Journal Article
T1 Bergman projection and BMO in hyperbolic metric: improvement of classical result.
A1 Rättyä, Jouni
A1 Peláez-Márquez, José Ángel
K1 Funciones de variable compleja
AB The Bergman projection $P_\alpha$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_\alpha: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the boundedness of the operator $P_\alpha:\BMO_2(\Delta)\to\mathcal{B}$, where $\BMO_2(\Delta)$ is the space of functions of bounded mean oscillation in the Bergman metric.We consider the Bergman projection $P_\omega$ and the space $\BMO_{\omega,p}(\Delta)$ of functions of bounded mean oscillation induced by $1<p<\infty$ and a radial weight $\omega\in\mathcal{M}$. Here $\mathcal{M}$ is a wide class of radial weights defined by means of moments of the weight, and it contains the standard and the exponential-type weights. We describe the weights such that $P_\omega:\BMO_{\omega,p}(\Delta)\to\mathcal{B}$ is bounded. They coincide with the weights for which $P_\omega: L^\infty \to \mathcal{B}$ is bounded and onto. This result seems to be new even for the standard radial weights when $p\ne2$.
PB Springer Nature
YR 2023
FD 2023
LK https://hdl.handle.net/10630/37351
UL https://hdl.handle.net/10630/37351
LA eng
NO Peláez, J.Á., Rättyä, J. Bergman projection and BMO in hyperbolic metric: improvement of classical result. Math. Z. 305, 19 (2023). https://doi.org/10.1007/s00209-023-03343-1
NO The research was supported in part by La Junta de Andalucía, project FQM210, and Vilho, Yrjö ja KalleVäisälä foundation of Finnish Academy of Science and Letters.
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 22 ene 2026