L^2(B_2,dμ_α(z))正交分解及Hankel型算子

The Orthogonal Decomposition of L^2 (B_2, dμ_α(z)) and Hankel Type Operators

令B2是2维复平面C2上的单位球，（α＞－1）是它上的加权测度．由Cauchy－Riemann算子观点和[1]中给出的三角域上的正交多项式，我们得到了正交分解和正交基，其中A0（＋，＋）和A0（－，－）分别是Bergman空间和共轭Bergman空间．利用单纯形上的正交多项式，可以将这种分解推广到L2（Bn，dμα（z））上去．另外，我们还得到了Hankel型算子的一些结果．

Let B2 be the unit ball of 2-dimensional complex plane C2, dμα(z) = dm(z)(α>-1) the weighted measure. From the view point of the Cauchy-Riemann operator and the triangle polynomial given in [1], we obtain an or thogonal decomposition and orthogonal basis, where A0(+,+) and A0(-, -) are the Bergman and anti-Bergman spaces respectively. This decomposition can be extended to L2(Bn, dμα(z)). In addi tion, we also obtain some results for Hankel type operators.