论文标题
玻色石laplacians，Bosonic Bergman和Hardy空间的多项式无效解决方案
Polynomial Null Solutions to Bosonic Laplacians, Bosonic Bergman and Hardy Spaces
论文作者
论文摘要
骨laplacian是Laplacian的概括，被构造为二阶与不变的差异操作员，作用于在特殊正交组的不可约表示的功能上，因此旋转组的值。在本文中，我们首先向能力介绍了一些均质多项式零解决方案，以给我们带来一些重要的结果，例如，多项式空间的正交分解是多项式空间的正交分解，以同质的多项式无效求解均应与Bosonic Laplacians相关。伯格曼空间，在更高的自旋空间中。也给出了单位球中玻色粒伯格曼空间的子核，并给出了玻感伯格曼投影的描述。最后，我们研究了玻感耐寒空间，这些空间被认为是谐波耐寒空间的概括。这里提供了一些谐波耐寒空间的一些已知结果的类似物。例如，连接到某些复杂的Borel测量空间，对玻色杆强烈空间功能的增长估计等等。
A bosonic Laplacian, which is a generalization of Laplacian, is constructed as a second order conformally invariant differential operator acting on functions taking values in irreducible representations of the special orthogonal group, hence of the spin group. In this paper, we firstly introduce some properties for homogeneous polynomial null solutions to bosonic Laplacians, which give us some important results, such as an orthogonal decomposition of the space of polynomials in terms of homogeneous polynomial null solutions to bosonic Laplacians, etc. This work helps us to introduce Bergman spaces related to bosonic Laplacians, named as bosonic Bergman spaces, in higher spin spaces. Reproducing kernels for bosonic Bergman spaces in the unit ball and a description of bosonic Bergman projection are given as well. At the end, we investigate bosonic Hardy spaces, which are considered as generalizations of harmonic Hardy spaces. Analogs of some well known results for harmonic Hardy spaces are provided here. For instance, connections to certain complex Borel measure spaces, growth estimates for functions in the bosonic Hardy spaces, etc.
