标题： 强凸域上Bergman空间的双重实现 显示英文标题

标题： Dual realizations of Bergman spaces on strongly convex domains

摘要： Fantappiè 变换和Laplace变换在凸紧集支撑的解析泛函与某些与$K\subset{\mathbb C}^n$和$K$相关的全纯函数空间之间建立了同构。将${\mathbb C}^n$中有界域的Bergman空间视为支撑在其闭包上的解析泛函空间的子空间，在平面情形下研究了这些变换限制的像。对于Fantappiè变换，这是针对单连通区域完成的（Napalkov Jr.--Yulumukhamtov，1995年）；对于Laplace变换，这是针对凸区域完成的（Napalkov Jr.--Yulumukhamtov，2004年）。本文中，我们在高维情形下研究强凸域的这一问题，并建立类似于平面情形的对偶结果。我们还给出了例子，表明平面情形的结果不能推广到高维的所有凸域。 显示英文摘要

摘要： The Fantappi\`e and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associated with $K$. Viewing the Bergman space of a bounded domain in ${\mathbb C}^n$ as a subspace of the space of analytic functionals supported on its closure, the images of the restrictions of these transforms have been studied in the planar setting. For the Fantappi\`e transform, this was done for simply connected domains (Napalkov Jr--Yulumukhamtov, 1995), and for the Laplace transform, this was done for convex domains (Napalkov Jr--Yulumukhamtov, 2004). In this paper, we study this problem in higher dimensions for strongly convex domains, and establish duality results analogous to the planar case. We also produce examples to show that the planar results cannot be generalized to all convex domains in higher dimensions.