Analytic Functions and Analytic Functionals on Some Balls in the Complex Euclidean Space

By generalizing the Lie norm, the Euclidean norm and the dual Lie norm, we could define a series of norms {N p }1≤p≤∞ on C n+1 (see [5] and [8]). Our results in [1], [2] and [3] for the Lie ball, the complex Euclidean ball and the dual Lie ball can be generalized for the N p -balls. In this note, following our paper [4], we consider analytic functions and analytic functionals on the N p -balls \({\tilde B_p}\left( r \right)\), and characterize them by their growth behavior of their harmonic components in their double series expansion.