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- W4283834460 abstract "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, $P_alpha: L^inftyto mathcal{B}$ is not a projection. This fact can be emended via the boundedness of the operator $P_alpha:BMO_2(Delta)tomathcal{B}$, 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 $omegainmathcal{M}$. 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 $P_omega:BMO_{omega,p}(Delta)tomathcal{B}$ 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 $pne2$." @default.
- W4283834460 created "2022-07-07" @default.
- W4283834460 creator A5056318177 @default.
- W4283834460 creator A5083223266 @default.
- W4283834460 date "2022-07-03" @default.
- W4283834460 modified "2023-09-26" @default.
- W4283834460 title "Bergman projection and BMO in hyperbolic metric -- improvement of classical result" @default.
- W4283834460 doi "https://doi.org/10.48550/arxiv.2207.01086" @default.
- W4283834460 hasPublicationYear "2022" @default.
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