论文标题
在坚固的核心和加权伯格曼空间的船体上$a_μ^1 $
On solid cores and hulls of weighted Bergman spaces $A_μ^1$
论文作者
论文摘要
我们考虑了单位光盘上的加权伯格曼空间$a_μ^1 $以及整个功能的相应空间，这些空间使用径向对称性的非原子borel测量定义。通过从反射伯格曼空间的情况下扩展技术，我们表征了$a_μ^1 $的实心核心。同样，由于实心$a_μ^1 $空间的特征，我们表明的是，在整个功能的情况下，确实存在实心$a_μ^1 $ - 空格。本文的第二部分仅限于单位光盘的情况，它包含$a_μ^1 $的实心船体的特征，当$μ$等于加权的lebesgue量与权重$ v $时。结果基于加权$ a^1 $ - 和$ h^\ infty $ - 空格的双重性关系，其有效性要求$ - \ log v $属于$ \ MATHCAL {W} _0 $ class $ - \ log v $，在许多出版物中研究；此外，$ v $必须满足作者介绍的条件$（b）$。指数降低权重$ v（z）= \ exp（-1 /（1- | z |）$提供了满足这两个假设的示例。
We consider weighted Bergman spaces $A_μ^1$ on the unit disc as well as the corresponding spaces of entire functions, defined using non-atomic Borel measures with radial symmetry. By extending the techniques from the case of reflexive Bergman spaces we characterize the solid core of $A_μ^1$. Also, as a consequence of a characterization of solid $A_μ^1$-spaces we show that, in the case of entire functions, there indeed exist solid $A_μ^1$-spaces. The second part of the paper is restricted to the case of the unit disc and it contains a characterization of the solid hull of $A_μ^1$, when $μ$ equals the weighted Lebesgue measure with weight $v$. The results are based on a duality relation of weighted $A^1$- and $H^\infty$-spaces, the validity of which requires the assumption that $- \log v$ belongs to the class $\mathcal{W}_0$, studied in a number of publications; moreover, $v$ has to satisfy condition $(b)$, introduced by the authors. The exponentially decreasing weight $v(z) = \exp( -1 /(1-|z|)$ provides an example satisfying both assumptions.
