Search

In this paper, we give the explicit formula for the zonal spherical function on the Lie ball in ℂn. [ABSTRACT FROM AUTHOR]

In this paper, we give the explicit formula for the zonal spherical function on the Lie ball in ℂn. [ABSTRACT FROM AUTHOR]

Let D={z∈n/1-2z¯zt+|zzt|2>0 and |zzt|<1} be the Lie ball in n and let Hq be the associated Hua operator. Then, for a complex number λ such that Re(iλ)>n/2-1, we establish that every function F satisfying the following Hua system of differential equations: [image omitted] is the Poisson transform of an Lp-function (1

Let and | zz t | 0, we establish that every &complexes;-valued function F on &Dscr; 2 satisfying the following Hua system of differential equations is the Poisson transform of an L 2 -function on the Shilov boundary S of &Dscr; 2 if and only if it satisfies the following growth condition of Hardy type: [ABSTRACT FROM AUTHOR]