论文标题
分析函数的平均径向可集成性空间
Average radial integrability spaces of analytic functions
论文作者
论文摘要
在本文中，我们介绍了$ rm（p，q）$，$ 1 \ leq p，q \ leq +\ infty $的家族。它们是平均径向可集成性的单位光盘中塑性功能的空间。这个家庭包含经典的耐寒空间（当$ p = \ infty $）和伯格曼空间（当$ p = q $）。我们根据参数在$ RM（P_1，Q_1）$（P_1，Q_1）$（P_2，Q_2）之间的包含表征。对于$ 1 <p，q <\ infty $，我们的主要结果通过伯格曼投影的界限来表征$ rm（p，q）$的双重空间（p，q）$。我们表明$ rm（p，q）$在且仅当$ q <+\ infty $时才可分开。实际上，我们提供了一种方法来构建$ \ ell^\ infty $ in $ rm（p，\ infty）$的同构副本。
In this paper we introduce the family of spaces $RM(p,q)$, $1\leq p,q\leq +\infty$. They are spaces of holomorphic functions in the unit disc with average radial integrability. This family contains the classical Hardy spaces (when $p=\infty$) and Bergman spaces (when $p=q$). We characterize the inclusion between $RM(p_1,q_1)$ and $RM(p_2,q_2)$ depending on the parameters. For $1<p,q<\infty$, our main result provides a characterization of the dual spaces of $RM(p,q)$ by means of the boundedness of the Bergman projection. We show that $RM(p,q)$ is separable if and only if $q<+\infty$. In fact, we provide a method to build isomorphic copies of $\ell^\infty$ in $RM(p,\infty)$.
