论文标题
Bergman投影和BMO双曲线度量 - 改进经典结果
Bergman projection and BMO in hyperbolic metric -- improvement of classical result
论文作者
论文摘要
由标准径向重量引起的Bergman投影$P_α$的界限是从$ l^\ infty $到Bloch Space $ \ Mathcal {B} $的。但是，$p_α：l^\ infty \ to \ mathcal {b} $不是投影。可以通过操作员$p_α的有界性来修改这一事实：bmo_2（δ）\ to \ mathcal {b} $，其中$ bmo_2（δ）$是伯格曼指标中有限均值振荡功能的功能的空间。 我们考虑伯格曼投影$p_Ω$和空间$ bmo_ {ω，p}（δ）$ themed均值振荡的函数，$ 1 <p <\ iffty $和径向重量$ω\ in \ Mathcal {m} $。这里$ \ Mathcal {M} $是通过重量矩定义的宽类径向重量，它包含标准和指数型重量。我们描述了$p_Ω的权重：bmo_ {ω，p}（δ）\ to \ mathcal {b} $是有限的。它们与$p_Ω：l^\ infty \ to \ mathcal {b} $的权重相吻合。即使对于标准的径向重量，当$ p \ ne2 $时，这个结果似乎也是新的。
The Bergman projection $P_α$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_α: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the boundedness of the operator $P_α:BMO_2(Δ)\to\mathcal{B}$, where $BMO_2(Δ)$ is the space of functions of bounded mean oscillation in the Bergman metric. We consider the Bergman projection $P_ω$ and the space $BMO_{ω,p}(Δ)$ of functions of bounded mean oscillation induced by $1<p<\infty$ and a radial weight $ω\in\mathcal{M}$. 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 $P_ω:BMO_{ω,p}(Δ)\to\mathcal{B}$ is bounded. They coincide with the weights for which $P_ω: L^\infty \to \mathcal{B}$ is bounded and onto. This result seems to be new even for the standard radial weights when $p\ne2$.
