广义Hartogs三角域上Bergman投影的 L^(p)正则性

L^(p) Regularity of the Bergman Projection on Generalizations of the Hartogs Triangle

在本文中,我们主要研究了一类C^(n+1)中的区域Ω_(k)^(n+1)={(z,w)∈C^(n)×C:|z|^(k)<|w|<1},其中k∈Z^(+),此区域是经典Hartogs三角域的推广.首先我们获得了这类域上Bergman核函数的显式公式,其次给出了使得Bergman投影L^(p)有界的p的取值范围,并且我们证明了p的这一范围是一个充分必要条件.

In this paper,we investigate a class of domainsΩ_(k)^(n+1)={(z,w)∈C^(n)×C:|z|^(k)<|w|<1}for k Z^(+) which generalizes the Hartogs triangle.We first obtain the new explicit formulas for the Bergman kernel function on these domains and further give a range of p values for which the L^(p) boundedness of the Bergman projection holds.This range of p is shown to be sharp。